diff --git a/crates/dapf/src/acceptance/load_testing.rs b/crates/dapf/src/acceptance/load_testing.rs
index e77fd5c8c..cf0d9966c 100644
--- a/crates/dapf/src/acceptance/load_testing.rs
+++ b/crates/dapf/src/acceptance/load_testing.rs
@@ -59,16 +59,16 @@ fn jobs_per_batch() -> impl Iterator<Item = usize> {
 fn vdaf_config_params() -> impl Iterator<Item = VdafConfig> {
     [
         VdafConfig::Prio2 { dimension: 99_992 },
-        VdafConfig::Prio3Draft09(
-            daphne::vdaf::Prio3Config::SumVecField64MultiproofHmacSha256Aes128 {
+        VdafConfig::Prio3(
+            daphne::vdaf::Prio3Config::Draft09SumVecField64MultiproofHmacSha256Aes128 {
                 bits: 1,
                 length: 100_000,
                 chunk_length: 320,
                 num_proofs: 2,
             },
         ),
-        VdafConfig::Prio3Draft09(
-            daphne::vdaf::Prio3Config::SumVecField64MultiproofHmacSha256Aes128 {
+        VdafConfig::Prio3(
+            daphne::vdaf::Prio3Config::Draft09SumVecField64MultiproofHmacSha256Aes128 {
                 bits: 1,
                 length: 100_000,
                 chunk_length: 320,
diff --git a/crates/dapf/src/acceptance/mod.rs b/crates/dapf/src/acceptance/mod.rs
index dc82028ab..d781da6fe 100644
--- a/crates/dapf/src/acceptance/mod.rs
+++ b/crates/dapf/src/acceptance/mod.rs
@@ -532,6 +532,7 @@ impl Test {
             agg_job_state,
             agg_job_resp,
             self.metrics(),
+            task_config.version,
         )?;
 
         let aggregated_report_count = agg_share_span
diff --git a/crates/dapf/src/cli_parsers.rs b/crates/dapf/src/cli_parsers.rs
index 80cbc7e82..4b3cbf2c6 100644
--- a/crates/dapf/src/cli_parsers.rs
+++ b/crates/dapf/src/cli_parsers.rs
@@ -58,22 +58,22 @@ impl DefaultVdafConfigs {
     fn into_vdaf_config(self) -> VdafConfig {
         match self {
             Self::Prio2Dimension99k => VdafConfig::Prio2 { dimension: 99_992 },
-            Self::Prio3Draft09NumProofs2 => {
-                VdafConfig::Prio3Draft09(Prio3Config::SumVecField64MultiproofHmacSha256Aes128 {
+            Self::Prio3Draft09NumProofs2 => VdafConfig::Prio3(
+                Prio3Config::Draft09SumVecField64MultiproofHmacSha256Aes128 {
                     bits: 1,
                     length: 100_000,
                     chunk_length: 320,
                     num_proofs: 2,
-                })
-            }
-            Self::Prio3Draft09NumProofs3 => {
-                VdafConfig::Prio3Draft09(Prio3Config::SumVecField64MultiproofHmacSha256Aes128 {
+                },
+            ),
+            Self::Prio3Draft09NumProofs3 => VdafConfig::Prio3(
+                Prio3Config::Draft09SumVecField64MultiproofHmacSha256Aes128 {
                     bits: 1,
                     length: 100_000,
                     chunk_length: 320,
                     num_proofs: 3,
-                })
-            }
+                },
+            ),
         }
     }
 }
diff --git a/crates/daphne-server/src/roles/mod.rs b/crates/daphne-server/src/roles/mod.rs
index 62a5de962..ec96287a8 100644
--- a/crates/daphne-server/src/roles/mod.rs
+++ b/crates/daphne-server/src/roles/mod.rs
@@ -186,32 +186,36 @@ mod test_utils {
                 cmd.vdaf.bits,
                 cmd.vdaf.length,
                 cmd.vdaf.chunk_length,
+                cmd.vdaf.dimension,
             ) {
-                ("Prio3Count", None, None, None) => VdafConfig::Prio3Draft09(Prio3Config::Count),
-                ("Prio3Sum", Some(bits), None, None) => VdafConfig::Prio3Draft09(Prio3Config::Sum {
-                    bits: bits.parse().map_err(|e| fatal_error!(err = ?e, "failed to parse bits for Prio3Config::Sum"))?,
+                ("Prio3Count", None, None, None, None) => VdafConfig::Prio3(Prio3Config::Count),
+                ("Prio3Sum", Some(max_measurement), None, None, None) => VdafConfig::Prio3(Prio3Config::Sum {
+                    max_measurement: max_measurement.parse().map_err(|e| fatal_error!(err = ?e, "failed to parse bits for Prio3Config::Sum"))?,
                 }),
-                ("Prio3SumVec", Some(bits), Some(length), Some(chunk_length)) => {
-                    VdafConfig::Prio3Draft09(Prio3Config::SumVec {
+                ("Prio3SumVec", Some(bits), Some(length), Some(chunk_length), None) => {
+                    VdafConfig::Prio3(Prio3Config::SumVec {
                         bits: bits.parse().map_err(|e| fatal_error!(err = ?e, "failed to parse bits for Prio3Config::SumVec"))?,
                         length: length.parse().map_err(|e| fatal_error!(err = ?e, "failed to parse length for Prio3Config::SumVec"))?,
                         chunk_length: chunk_length.parse().map_err(|e| fatal_error!(err = ?e, "failed to parse chunk_length for Prio3Config::SumVec"))?,
                     })
                 }
-                ("Prio3Histogram", None, Some(length), Some(chunk_length)) => {
-                    VdafConfig::Prio3Draft09(Prio3Config::Histogram {
+                ("Prio3Histogram", None, Some(length), Some(chunk_length), None) => {
+                    VdafConfig::Prio3(Prio3Config::Histogram {
                         length: length.parse().map_err(|e| fatal_error!(err = ?e, "failed to parse length for Prio3Config::Histogram"))?,
                         chunk_length: chunk_length.parse().map_err(|e| fatal_error!(err = ?e, "failed to parse chunk_length for Prio3Config::Histogram"))?,
                     })
                 }
-                ("Prio3SumVecField64MultiproofHmacSha256Aes128", Some(bits), Some(length), Some(chunk_length)) => {
-                    VdafConfig::Prio3Draft09(Prio3Config::SumVecField64MultiproofHmacSha256Aes128 {
+                ("Prio3SumVecField64MultiproofHmacSha256Aes128", Some(bits), Some(length), Some(chunk_length), None) => {
+                    VdafConfig::Prio3(Prio3Config::Draft09SumVecField64MultiproofHmacSha256Aes128 {
                         bits: bits.parse().map_err(|e| fatal_error!(err = ?e, "failed to parse bits for Prio3Config::SumVecField64MultiproofHmacSha256Aes128"))?,
                         length: length.parse().map_err(|e| fatal_error!(err = ?e, "failed to parse length for Prio3Config::SumVecField64MultiproofHmacSha256Aes128"))?,
                         chunk_length: chunk_length.parse().map_err(|e| fatal_error!(err = ?e, "failed to parse chunk_length for Prio3Config::SumVecField64MultiproofHmacSha256Aes128"))?,
                         num_proofs: 2,
                     })
                 }
+                ("Prio2", None, None, None, Some(dimension)) => VdafConfig::Prio2 {
+                    dimension: dimension.parse().map_err(|e| fatal_error!(err = ?e, "failed to parse dimension for Prio2"))?,
+                },
                 _ => return Err(fatal_error!(err = "command failed: unrecognized VDAF")),
             };
 
diff --git a/crates/daphne-server/tests/e2e/e2e.rs b/crates/daphne-server/tests/e2e/e2e.rs
index 93a4ca009..309bc6d7f 100644
--- a/crates/daphne-server/tests/e2e/e2e.rs
+++ b/crates/daphne-server/tests/e2e/e2e.rs
@@ -151,7 +151,6 @@ async fn hpke_configs_are_cached(version: DapVersion) {
 
 async_test_versions! { hpke_configs_are_cached }
 
-// TODO draft02 cleanup: In draft09, the client is meant to PUT its report, not POST it.
 async fn leader_upload(version: DapVersion) {
     let t = TestRunner::default_with_version(version).await;
     let mut rng = thread_rng();
@@ -171,7 +170,7 @@ async fn leader_upload(version: DapVersion) {
             &hpke_config_list,
             t.now,
             &t.task_id,
-            DapMeasurement::U64(23),
+            DapMeasurement::U32Vec(vec![1; 10]),
             version,
         )
         .unwrap();
@@ -202,7 +201,7 @@ async fn leader_upload(version: DapVersion) {
                 &hpke_config_list,
                 t.now,
                 &bad_id,
-                DapMeasurement::U64(999),
+                DapMeasurement::U32Vec(vec![1; 10]),
                 version,
             )
             .unwrap()
@@ -222,7 +221,7 @@ async fn leader_upload(version: DapVersion) {
             &hpke_config_list,
             t.now,
             &t.task_id,
-            DapMeasurement::U64(999),
+            DapMeasurement::U32Vec(vec![1; 10]),
             version,
         )
         .unwrap();
@@ -264,7 +263,7 @@ async fn leader_upload(version: DapVersion) {
             &hpke_config_list,
             t.task_config.not_after, // past the expiration date
             &t.task_id,
-            DapMeasurement::U64(23),
+            DapMeasurement::U32Vec(vec![1; 10]),
             version,
         )
         .unwrap();
@@ -352,7 +351,7 @@ async fn leader_back_compat_upload(version: DapVersion) {
             &hpke_config_list,
             t.now,
             &t.task_id,
-            DapMeasurement::U64(23),
+            DapMeasurement::U32Vec(vec![0; 10]),
             version,
         )
         .unwrap();
@@ -561,7 +560,7 @@ async fn internal_leader_process(version: DapVersion) {
                     &hpke_config_list,
                     now,
                     &t.task_id,
-                    DapMeasurement::U64(1),
+                    DapMeasurement::U32Vec(vec![1; 10]),
                     version,
                 )
                 .unwrap()
@@ -641,7 +640,7 @@ async fn leader_collect_ok(version: DapVersion) {
                     &hpke_config_list,
                     now,
                     &t.task_id,
-                    DapMeasurement::U64(1),
+                    DapMeasurement::U32Vec(vec![1; 10]),
                     version,
                 )
                 .unwrap()
@@ -707,7 +706,10 @@ async fn leader_collect_ok(version: DapVersion) {
         .unwrap();
     assert_eq!(
         agg_res,
-        DapAggregateResult::U128(u128::from(t.task_config.min_batch_size))
+        DapAggregateResult::U32Vec(vec![
+            u32::try_from(t.task_config.min_batch_size).unwrap();
+            10
+        ])
     );
 
     // Check that the time interval for the reports is correct.
@@ -739,7 +741,7 @@ async fn leader_collect_ok(version: DapVersion) {
     //      "upload",
     //      DapMediaType::Report,
     //      t.task_config.vdaf
-    //          .produce_report(&hpke_config_list, now, &t.task_id, DapMeasurement::U64(1))
+    //          .produce_report(&hpke_config_list, now, &t.task_id, DapMeasurement::U32Vec(vec![1; 10]))
     //          .unwrap()
     //          .get_encoded(),
     //      400,
@@ -779,7 +781,7 @@ async fn leader_collect_ok_interleaved(version: DapVersion) {
                     &hpke_config_list,
                     now,
                     &t.task_id,
-                    DapMeasurement::U64(1),
+                    DapMeasurement::U32Vec(vec![1; 10]),
                     version,
                 )
                 .unwrap()
@@ -843,7 +845,7 @@ async fn leader_collect_not_ready_min_batch_size(version: DapVersion) {
                     &hpke_config_list,
                     now,
                     &t.task_id,
-                    DapMeasurement::U64(1),
+                    DapMeasurement::U32Vec(vec![1; 10]),
                     version,
                 )
                 .unwrap()
@@ -936,7 +938,7 @@ async fn leader_collect_back_compat(version: DapVersion) {
                     &hpke_config_list,
                     now,
                     &t.task_id,
-                    DapMeasurement::U64(1),
+                    DapMeasurement::U32Vec(vec![1; 10]),
                     version,
                 )
                 .unwrap()
@@ -1091,7 +1093,7 @@ async fn leader_collect_abort_overlapping_batch_interval(version: DapVersion) {
                     &hpke_config_list,
                     now,
                     &t.task_id,
-                    DapMeasurement::U64(1),
+                    DapMeasurement::U32Vec(vec![1; 10]),
                     version,
                 )
                 .unwrap()
@@ -1187,7 +1189,7 @@ async fn leader_selected() {
                     &hpke_config_list,
                     t.now,
                     &t.task_id,
-                    DapMeasurement::U64(1),
+                    DapMeasurement::U32Vec(vec![1; 10]),
                     version,
                 )
                 .unwrap()
@@ -1256,7 +1258,10 @@ async fn leader_selected() {
         .unwrap();
     assert_eq!(
         agg_res,
-        DapAggregateResult::U128(u128::from(t.task_config.min_batch_size))
+        DapAggregateResult::U32Vec(vec![
+            u32::try_from(t.task_config.min_batch_size).unwrap();
+            10
+        ])
     );
 
     // Collector: Poll the collect URI once more. Expect the response to be the same as the first,
@@ -1282,7 +1287,7 @@ async fn leader_selected() {
                     &hpke_config_list,
                     t.now,
                     &t.task_id,
-                    DapMeasurement::U64(1),
+                    DapMeasurement::U32Vec(vec![1; 10]),
                     version,
                 )
                 .unwrap()
diff --git a/crates/daphne-server/tests/e2e/test_runner.rs b/crates/daphne-server/tests/e2e/test_runner.rs
index be798032d..e39c33a85 100644
--- a/crates/daphne-server/tests/e2e/test_runner.rs
+++ b/crates/daphne-server/tests/e2e/test_runner.rs
@@ -10,7 +10,7 @@ use daphne::{
         encode_base64url, taskprov::TaskprovAdvertisement, Base64Encode, BatchId, CollectionJobId,
         Duration, HpkeConfigList, Interval, TaskId,
     },
-    vdaf::{Prio3Config, VdafConfig},
+    vdaf::VdafConfig,
     DapBatchMode, DapGlobalConfig, DapLeaderProcessTelemetry, DapTaskConfig, DapVersion,
 };
 use daphne_service_utils::http_headers;
@@ -29,7 +29,8 @@ use std::{
 use tokio::time::timeout;
 use url::Url;
 
-const VDAF_CONFIG: &VdafConfig = &VdafConfig::Prio3Draft09(Prio3Config::Sum { bits: 10 });
+// Use a VDAF that is supported in all versions of DAP.
+const VDAF_CONFIG: &VdafConfig = &VdafConfig::Prio2 { dimension: 10 };
 pub(crate) const MIN_BATCH_SIZE: u64 = 10;
 pub(crate) const MAX_BATCH_SIZE: u32 = 12;
 pub(crate) const TIME_PRECISION: Duration = 3600; // seconds
@@ -167,10 +168,10 @@ impl TestRunner {
             encode_base64url(t.collector_hpke_receiver.config.get_encoded().unwrap());
 
         let vdaf = json!({
-            "type": "Prio3Sum",
-            "bits": assert_matches!(
+            "type": "Prio2",
+            "dimension": assert_matches!(
                 t.task_config.vdaf,
-                VdafConfig::Prio3Draft09(Prio3Config::Sum{ bits }) => format!("{bits}")
+                VdafConfig::Prio2{ dimension } => format!("{dimension}")
             ),
         });
 
diff --git a/crates/daphne-service-utils/src/test_route_types.rs b/crates/daphne-service-utils/src/test_route_types.rs
index 30c22f1b1..3fba74fde 100644
--- a/crates/daphne-service-utils/src/test_route_types.rs
+++ b/crates/daphne-service-utils/src/test_route_types.rs
@@ -30,34 +30,44 @@ pub struct InternalTestVdaf {
     pub length: Option<String>,
     #[serde(skip_serializing_if = "Option::is_none")]
     pub chunk_length: Option<String>,
+    #[serde(skip_serializing_if = "Option::is_none")]
+    pub dimension: Option<String>,
 }
 
 impl From<VdafConfig> for InternalTestVdaf {
     fn from(vdaf: VdafConfig) -> Self {
-        let (typ, bits, length, chunk_length) = match vdaf {
-            VdafConfig::Prio3Draft09(prio3) => match prio3 {
-                Prio3Config::Count => ("Prio3Draft09Count", None, None, None),
-                Prio3Config::Sum { bits } => ("Prio3Draft09Sum", Some(bits), None, None),
+        let (typ, bits, length, chunk_length, dimension) = match vdaf {
+            VdafConfig::Prio3(prio3) => match prio3 {
+                Prio3Config::Count => ("Prio3Count", None, None, None, None),
+                Prio3Config::Sum { max_measurement } => (
+                    "Prio3Sum",
+                    Some(usize::try_from(max_measurement).unwrap()),
+                    None,
+                    None,
+                    None,
+                ),
                 Prio3Config::Histogram {
                     length,
                     chunk_length,
                 } => (
-                    "Prio3Draft09Histogram",
+                    "Prio3Histogram",
                     None,
                     Some(length),
                     Some(chunk_length),
+                    None,
                 ),
                 Prio3Config::SumVec {
                     bits,
                     length,
                     chunk_length,
                 } => (
-                    "Prio3Draft09SumVec",
+                    "Prio3SumVec",
                     Some(bits),
                     Some(length),
                     Some(chunk_length),
+                    None,
                 ),
-                Prio3Config::SumVecField64MultiproofHmacSha256Aes128 {
+                Prio3Config::Draft09SumVecField64MultiproofHmacSha256Aes128 {
                     bits,
                     length,
                     chunk_length,
@@ -67,34 +77,11 @@ impl From<VdafConfig> for InternalTestVdaf {
                     Some(bits),
                     Some(length),
                     Some(chunk_length),
+                    None,
                 ),
             },
-            VdafConfig::Prio3(prio3) => match prio3 {
-                Prio3Config::Count => ("Prio3Count", None, None, None),
-                Prio3Config::Sum { bits } => ("Prio3Sum", Some(bits), None, None),
-                Prio3Config::Histogram {
-                    length,
-                    chunk_length,
-                } => ("Prio3Histogram", None, Some(length), Some(chunk_length)),
-                Prio3Config::SumVec {
-                    bits,
-                    length,
-                    chunk_length,
-                } => ("Prio3SumVec", Some(bits), Some(length), Some(chunk_length)),
-                Prio3Config::SumVecField64MultiproofHmacSha256Aes128 {
-                    bits,
-                    length,
-                    chunk_length,
-                    num_proofs: _unimplemented,
-                } => (
-                    "Prio3SumVecField64MultiproofHmacSha256Aes128",
-                    Some(bits),
-                    Some(length),
-                    Some(chunk_length),
-                ),
-            },
-            VdafConfig::Prio2 { .. } => ("Prio2", None, None, None),
-            VdafConfig::Pine(_) => ("Pine", None, None, None),
+            VdafConfig::Prio2 { dimension } => ("Prio2", None, None, None, Some(dimension)),
+            VdafConfig::Pine(_) => ("Pine", None, None, None, None),
             #[cfg(feature = "experimental")]
             VdafConfig::Mastic { .. } => todo!(),
         };
@@ -103,6 +90,7 @@ impl From<VdafConfig> for InternalTestVdaf {
             bits: bits.map(|a| a.to_string()),
             length: length.map(|a| a.to_string()),
             chunk_length: chunk_length.map(|a| a.to_string()),
+            dimension: dimension.map(|a| a.to_string()),
         }
     }
 }
diff --git a/crates/daphne/benches/aggregation.rs b/crates/daphne/benches/aggregation.rs
index 2ae70556d..318e15add 100644
--- a/crates/daphne/benches/aggregation.rs
+++ b/crates/daphne/benches/aggregation.rs
@@ -37,18 +37,20 @@ fn consume_reports_vary_vdaf_dimension(c: &mut Criterion) {
     let mut test = AggregationJobTest::new(
         &VdafConfig::Prio2 { dimension: 0 },
         HpkeKemId::P256HkdfSha256,
-        DapVersion::Latest,
+        DapVersion::Draft09,
     );
     test.disable_replay_protection();
 
     let mut g = c.benchmark_group(function!());
     for vdaf_length in vdaf_lengths {
-        let vdaf = VdafConfig::Prio3Draft09(Prio3Config::SumVecField64MultiproofHmacSha256Aes128 {
-            bits: 1,
-            length: vdaf_length,
-            chunk_length: 320,
-            num_proofs: 2,
-        });
+        let vdaf = VdafConfig::Prio3(
+            Prio3Config::Draft09SumVecField64MultiproofHmacSha256Aes128 {
+                bits: 1,
+                length: vdaf_length,
+                chunk_length: 320,
+                num_proofs: 2,
+            },
+        );
         test.change_vdaf(vdaf);
         let reports = test
             .produce_repeated_reports(vdaf.gen_measurement().unwrap())
@@ -66,15 +68,16 @@ fn consume_reports_vary_vdaf_dimension(c: &mut Criterion) {
 }
 
 fn consume_reports_vary_num_reports(c: &mut Criterion) {
-    const VDAF: VdafConfig =
-        VdafConfig::Prio3Draft09(Prio3Config::SumVecField64MultiproofHmacSha256Aes128 {
+    const VDAF: VdafConfig = VdafConfig::Prio3(
+        Prio3Config::Draft09SumVecField64MultiproofHmacSha256Aes128 {
             bits: 1,
             length: 1000,
             chunk_length: 320,
             num_proofs: 2,
-        });
+        },
+    );
 
-    let mut test = AggregationJobTest::new(&VDAF, HpkeKemId::P256HkdfSha256, DapVersion::Latest);
+    let mut test = AggregationJobTest::new(&VDAF, HpkeKemId::P256HkdfSha256, DapVersion::Draft09);
     test.disable_replay_protection();
 
     let mut g = c.benchmark_group(function!());
diff --git a/crates/daphne/src/protocol/aggregator.rs b/crates/daphne/src/protocol/aggregator.rs
index dc21fc315..124863ddf 100644
--- a/crates/daphne/src/protocol/aggregator.rs
+++ b/crates/daphne/src/protocol/aggregator.rs
@@ -21,8 +21,6 @@ use crate::{
     protocol::{decode_ping_pong_framed, PingPongMessageType},
     vdaf::{
         prio2::{prio2_prep_finish, prio2_prep_finish_from_shares},
-        prio3::{prio3_prep_finish, prio3_prep_finish_from_shares},
-        prio3_draft09::{prio3_draft09_prep_finish, prio3_draft09_prep_finish_from_shares},
         VdafError,
     },
     AggregationJobReportState, DapAggregateShare, DapAggregateSpan, DapAggregationJobState,
@@ -286,6 +284,7 @@ impl DapTaskConfig {
         report_status: &HashMap<ReportId, ReportProcessedStatus>,
         part_batch_sel: &PartialBatchSelector,
         initialized_reports: &[InitializedReport<WithPeerPrepShare>],
+        version: DapVersion,
     ) -> Result<(DapAggregateSpan<DapAggregateShare>, AggregationJobResp), DapError> {
         let num_reports = initialized_reports.len();
         let mut agg_span = DapAggregateSpan::default();
@@ -304,23 +303,15 @@ impl DapTaskConfig {
                         prep_state: helper_prep_state,
                     } => {
                         let res = match &self.vdaf {
-                            VdafConfig::Prio3Draft09(prio3_config) => {
-                                prio3_draft09_prep_finish_from_shares(
-                                    prio3_config,
+                            VdafConfig::Prio3(prio3_config) => prio3_config
+                                .prep_finish_from_shares(
+                                    version,
                                     1,
+                                    task_id,
                                     helper_prep_state.clone(),
                                     helper_prep_share.clone(),
                                     leader_prep_share,
-                                )
-                            }
-                            VdafConfig::Prio3(prio3_config) => prio3_prep_finish_from_shares(
-                                prio3_config,
-                                1,
-                                task_id,
-                                helper_prep_state.clone(),
-                                helper_prep_share.clone(),
-                                leader_prep_share,
-                            ),
+                                ),
                             VdafConfig::Prio2 { dimension } => prio2_prep_finish_from_shares(
                                 *dimension,
                                 helper_prep_state.clone(),
@@ -406,6 +397,7 @@ impl DapTaskConfig {
         state: DapAggregationJobState,
         agg_job_resp: AggregationJobResp,
         metrics: &dyn DaphneMetrics,
+        version: DapVersion,
     ) -> Result<DapAggregateSpan<DapAggregateShare>, DapError> {
         if agg_job_resp.transitions.len() != state.seq.len() {
             return Err(DapAbort::InvalidMessage {
@@ -459,11 +451,8 @@ impl DapTaskConfig {
             };
 
             let res = match &self.vdaf {
-                VdafConfig::Prio3Draft09(prio3_config) => {
-                    prio3_draft09_prep_finish(prio3_config, leader.prep_state, prep_msg)
-                }
                 VdafConfig::Prio3(prio3_config) => {
-                    prio3_prep_finish(prio3_config, leader.prep_state, prep_msg, *task_id)
+                    prio3_config.prep_finish(leader.prep_state, prep_msg, *task_id, version)
                 }
                 VdafConfig::Prio2 { dimension } => {
                     prio2_prep_finish(*dimension, leader.prep_state, prep_msg)
diff --git a/crates/daphne/src/protocol/client.rs b/crates/daphne/src/protocol/client.rs
index 97a5b6604..349c380f1 100644
--- a/crates/daphne/src/protocol/client.rs
+++ b/crates/daphne/src/protocol/client.rs
@@ -7,7 +7,7 @@ use crate::{
     constants::DapAggregatorRole,
     hpke::{info_and_aad, HpkeConfig},
     messages::{Extension, PlaintextInputShare, Report, ReportId, ReportMetadata, TaskId, Time},
-    vdaf::{prio2::prio2_shard, prio3::prio3_shard, prio3_draft09::prio3_draft09_shard, VdafError},
+    vdaf::{prio2::prio2_shard, VdafError},
     DapError, DapMeasurement, DapVersion, VdafConfig,
 };
 use prio::codec::ParameterizedEncode;
@@ -45,7 +45,7 @@ impl VdafConfig {
         let mut rng = thread_rng();
         let report_id = ReportId(rng.gen());
         let (public_share, input_shares) = self
-            .produce_input_shares(measurement, &report_id.0, task_id)
+            .produce_input_shares(measurement, &report_id.0, task_id, version)
             .map_err(DapError::from_vdaf)?;
         Self::produce_report_with_extensions_for_shares(
             public_share,
@@ -122,13 +122,11 @@ impl VdafConfig {
         measurement: DapMeasurement,
         nonce: &[u8; 16],
         task_id: &TaskId,
+        version: DapVersion,
     ) -> Result<(Vec<u8>, [Vec<u8>; 2]), VdafError> {
         match self {
-            Self::Prio3Draft09(prio3_config) => {
-                Ok(prio3_draft09_shard(prio3_config, measurement, nonce)?)
-            }
             Self::Prio3(prio3_config) => {
-                Ok(prio3_shard(prio3_config, measurement, nonce, *task_id)?)
+                Ok(prio3_config.shard(version, measurement, nonce, *task_id)?)
             }
             Self::Prio2 { dimension } => Ok(prio2_shard(*dimension, measurement, nonce)?),
             #[cfg(feature = "experimental")]
diff --git a/crates/daphne/src/protocol/collector.rs b/crates/daphne/src/protocol/collector.rs
index 3dfca90c9..f6fc6a88f 100644
--- a/crates/daphne/src/protocol/collector.rs
+++ b/crates/daphne/src/protocol/collector.rs
@@ -8,7 +8,7 @@ use crate::{
     fatal_error,
     hpke::{info_and_aad, HpkeDecrypter},
     messages::{BatchSelector, HpkeCiphertext, TaskId},
-    vdaf::{prio2::prio2_unshard, prio3::prio3_unshard, prio3_draft09::prio3_draft09_unshard},
+    vdaf::prio2::prio2_unshard,
     DapAggregateResult, DapAggregationParam, DapError, DapVersion, VdafConfig,
 };
 
@@ -73,10 +73,9 @@ impl VdafConfig {
 
         let num_measurements = usize::try_from(report_count).unwrap();
         match self {
-            Self::Prio3Draft09(prio3_config) => {
-                prio3_draft09_unshard(prio3_config, num_measurements, agg_shares)
+            Self::Prio3(prio3_config) => {
+                prio3_config.unshard(version, num_measurements, agg_shares)
             }
-            Self::Prio3(prio3_config) => prio3_unshard(prio3_config, num_measurements, agg_shares),
             Self::Prio2 { dimension } => prio2_unshard(*dimension, num_measurements, agg_shares),
             #[cfg(feature = "experimental")]
             Self::Mastic {
diff --git a/crates/daphne/src/protocol/mod.rs b/crates/daphne/src/protocol/mod.rs
index 64eadd55d..47627e7bc 100644
--- a/crates/daphne/src/protocol/mod.rs
+++ b/crates/daphne/src/protocol/mod.rs
@@ -72,7 +72,7 @@ mod test {
         },
         test_versions,
         testing::AggregationJobTest,
-        vdaf::{Prio3Config, VdafConfig},
+        vdaf::VdafConfig,
         DapAggregateResult, DapAggregateShare, DapAggregationParam, DapError, DapMeasurement,
         DapVersion, VdafAggregateShare, VdafPrepShare, VdafPrepState,
     };
@@ -80,24 +80,17 @@ mod test {
     use hpke_rs::HpkePublicKey;
     use prio::{
         codec::encode_u32_items,
+        field::FieldPrio2,
         vdaf::{
-            prio3::Prio3, Aggregator as VdafAggregator, Collector as VdafCollector,
-            PrepareTransition,
-        },
-    };
-    use prio_draft09::{
-        field::Field64 as Field64Draft09,
-        vdaf::{
-            prio3::Prio3 as Prio3Draft09, AggregateShare as AggregateShareDraft09,
-            Aggregator as VdafAggregatorDraft09, Collector as VdafCollectorDraft09,
-            OutputShare as OutputShareDraft09, PrepareTransition as PrepareTransitionDraft09,
+            prio2::Prio2, AggregateShare, Aggregator as VdafAggregator, Collector as VdafCollector,
+            OutputShare, PrepareTransition,
         },
     };
     use rand::prelude::*;
     use std::iter::zip;
 
-    const TEST_VDAF: &VdafConfig = &VdafConfig::Prio3(Prio3Config::Count);
-    const TEST_VDAF_DRAFT09: &VdafConfig = &VdafConfig::Prio3Draft09(Prio3Config::Count);
+    // Choose a VDAF for testing that is supported by all versions of DAP.
+    const TEST_VDAF: &VdafConfig = &VdafConfig::Prio2 { dimension: 10 };
 
     fn roundtrip_report(version: DapVersion) {
         let t = AggregationJobTest::new(TEST_VDAF, HpkeKemId::X25519HkdfSha256, version);
@@ -108,7 +101,7 @@ mod test {
                 &t.client_hpke_config_list,
                 t.now,
                 &t.task_id,
-                DapMeasurement::U64(1),
+                DapMeasurement::U32Vec(vec![1; 10]),
                 t.task_config.version,
             )
             .unwrap();
@@ -170,26 +163,23 @@ mod test {
             helper_prep_share,
         ) {
             (
-                VdafPrepState::Prio3Field64(leader_step),
-                VdafPrepState::Prio3Field64(helper_step),
-                VdafPrepShare::Prio3Field64(leader_share),
-                VdafPrepShare::Prio3Field64(helper_share),
+                VdafPrepState::Prio2(leader_step),
+                VdafPrepState::Prio2(helper_step),
+                VdafPrepShare::Prio2(leader_share),
+                VdafPrepShare::Prio2(helper_share),
             ) => {
-                let ctx = &["dap-13".as_bytes(), &t.task_id.0].concat();
-                //let ctx = binding.as_slice();
-                let vdaf = Prio3::new_count(2).unwrap();
-                let message = vdaf
-                    .prepare_shares_to_prepare_message(ctx, &(), [leader_share, helper_share])
+                let vdaf = Prio2::new(10).unwrap();
+                vdaf.prepare_shares_to_prepare_message(&[], &(), [leader_share, helper_share])
                     .unwrap();
 
                 let leader_out_share = assert_matches!(
-                    vdaf.prepare_next(ctx, leader_step, message.clone()).unwrap(),
+                    vdaf.prepare_next(&[], leader_step, ()).unwrap(),
                     PrepareTransition::Finish(out_share) => out_share
                 );
                 let leader_agg_share = vdaf.aggregate(&(), [leader_out_share]).unwrap();
 
                 let helper_out_share = assert_matches!(
-                    vdaf.prepare_next(ctx, helper_step, message).unwrap(),
+                    vdaf.prepare_next(&[], helper_step, ()).unwrap(),
                     PrepareTransition::Finish(out_share) => out_share
                 );
                 let helper_agg_share = vdaf.aggregate(&(), [helper_out_share]).unwrap();
@@ -197,7 +187,7 @@ mod test {
                 assert_eq!(
                     vdaf.unshard(&(), vec![leader_agg_share, helper_agg_share], 1)
                         .unwrap(),
-                    1,
+                    vec![1; 10],
                 );
             }
             _ => {
@@ -208,113 +198,6 @@ mod test {
 
     test_versions! { roundtrip_report }
 
-    #[test]
-    fn roundtrip_report_vdaf_draft09() {
-        let version = DapVersion::Draft09;
-        let t = AggregationJobTest::new(TEST_VDAF_DRAFT09, HpkeKemId::X25519HkdfSha256, version);
-        let report = t
-            .task_config
-            .vdaf
-            .produce_report(
-                &t.client_hpke_config_list,
-                t.now,
-                &t.task_id,
-                DapMeasurement::U64(1),
-                t.task_config.version,
-            )
-            .unwrap();
-
-        let [leader_share, helper_share] = report.encrypted_input_shares;
-
-        let InitializedReport::Ready {
-            prep_share: leader_prep_share,
-            prep_state: leader_prep_state,
-            ..
-        } = InitializedReport::from_client(
-            &t.leader_hpke_receiver_config,
-            t.valid_report_time_range(),
-            &t.task_id,
-            &t.task_config,
-            ReportShare {
-                report_metadata: report.report_metadata.clone(),
-                public_share: report.public_share.clone(),
-                encrypted_input_share: leader_share,
-            },
-            &DapAggregationParam::Empty,
-        )
-        .unwrap()
-        else {
-            panic!("rejected unexpectedly");
-        };
-
-        let InitializedReport::Ready {
-            prep_share: helper_prep_share,
-            prep_state: helper_prep_state,
-            ..
-        } = InitializedReport::from_leader(
-            &t.helper_hpke_receiver_config,
-            t.valid_report_time_range(),
-            &t.task_id,
-            &t.task_config,
-            ReportShare {
-                report_metadata: report.report_metadata,
-                public_share: report.public_share,
-                encrypted_input_share: helper_share,
-            },
-            {
-                let mut outbound = Vec::new();
-                outbound.push(PingPongMessageType::Initialize as u8);
-                encode_u32_items(&mut outbound, &version, &[leader_prep_share.clone()]).unwrap();
-                outbound
-            },
-            &DapAggregationParam::Empty,
-        )
-        .unwrap()
-        else {
-            panic!("rejected unexpectedly");
-        };
-
-        match (
-            leader_prep_state,
-            helper_prep_state,
-            leader_prep_share,
-            helper_prep_share,
-        ) {
-            (
-                VdafPrepState::Prio3Draft09Field64(leader_step),
-                VdafPrepState::Prio3Draft09Field64(helper_step),
-                VdafPrepShare::Prio3Draft09Field64(leader_share),
-                VdafPrepShare::Prio3Draft09Field64(helper_share),
-            ) => {
-                let vdaf = Prio3Draft09::new_count(2).unwrap();
-                let message = vdaf
-                    .prepare_shares_to_prepare_message(&(), [leader_share, helper_share])
-                    .unwrap();
-
-                let leader_out_share = assert_matches!(
-                    vdaf.prepare_next(leader_step, message.clone()).unwrap(),
-                    PrepareTransitionDraft09::Finish(out_share) => out_share
-                );
-                let leader_agg_share = vdaf.aggregate(&(), [leader_out_share]).unwrap();
-
-                let helper_out_share = assert_matches!(
-                    vdaf.prepare_next(helper_step, message).unwrap(),
-                    PrepareTransitionDraft09::Finish(out_share) => out_share
-                );
-                let helper_agg_share = vdaf.aggregate(&(), [helper_out_share]).unwrap();
-
-                assert_eq!(
-                    vdaf.unshard(&(), vec![leader_agg_share, helper_agg_share], 1)
-                        .unwrap(),
-                    1,
-                );
-            }
-            _ => {
-                panic!("unexpected output from leader or helper");
-            }
-        }
-    }
-
     fn roundtrip_report_unsupported_hpke_suite(version: DapVersion) {
         let t = AggregationJobTest::new(TEST_VDAF, HpkeKemId::X25519HkdfSha256, version);
 
@@ -334,7 +217,7 @@ mod test {
             &unsupported_hpke_config_list,
             t.now,
             &t.task_id,
-            DapMeasurement::U64(1),
+            DapMeasurement::U32Vec(vec![1; 10]),
             t.task_config.version,
         );
         assert_matches!(
@@ -348,9 +231,9 @@ mod test {
     fn produce_agg_job_req(version: DapVersion) {
         let t = AggregationJobTest::new(TEST_VDAF, HpkeKemId::X25519HkdfSha256, version);
         let reports = t.produce_reports(vec![
-            DapMeasurement::U64(1),
-            DapMeasurement::U64(0),
-            DapMeasurement::U64(0),
+            DapMeasurement::U32Vec(vec![1; 10]),
+            DapMeasurement::U32Vec(vec![0; 10]),
+            DapMeasurement::U32Vec(vec![0; 10]),
         ]);
 
         let (agg_job_state, agg_job_init_req) =
@@ -374,7 +257,7 @@ mod test {
 
     fn produce_agg_job_req_skip_hpke_decrypt_err(version: DapVersion) {
         let t = AggregationJobTest::new(TEST_VDAF, HpkeKemId::X25519HkdfSha256, version);
-        let mut reports = t.produce_reports(vec![DapMeasurement::U64(1)]);
+        let mut reports = t.produce_reports(vec![DapMeasurement::U32Vec(vec![0; 10])]);
 
         // Simulate HPKE decryption error of leader's report share.
         reports[0].encrypted_input_shares[0].payload[0] ^= 1;
@@ -399,7 +282,7 @@ mod test {
                 &t.client_hpke_config_list,
                 t.valid_report_time_range().start - 1,
                 &t.task_id,
-                DapMeasurement::U64(1),
+                DapMeasurement::U32Vec(vec![1; 10]),
                 t.task_config.version,
             )
             .unwrap()];
@@ -424,7 +307,7 @@ mod test {
                 &t.client_hpke_config_list,
                 t.valid_report_time_range().end + 1,
                 &t.task_id,
-                DapMeasurement::U64(1),
+                DapMeasurement::U32Vec(vec![1; 10]),
                 t.task_config.version,
             )
             .unwrap()];
@@ -442,7 +325,7 @@ mod test {
 
     fn produce_agg_job_req_skip_hpke_unknown_config_id(version: DapVersion) {
         let t = AggregationJobTest::new(TEST_VDAF, HpkeKemId::X25519HkdfSha256, version);
-        let mut reports = t.produce_reports(vec![DapMeasurement::U64(1)]);
+        let mut reports = t.produce_reports(vec![DapMeasurement::U32Vec(vec![1; 10])]);
 
         // Client tries to send Leader encrypted input with incorrect config ID.
         reports[0].encrypted_input_shares[0].config_id ^= 1;
@@ -461,8 +344,14 @@ mod test {
     fn produce_agg_job_req_skip_vdaf_prep_error(version: DapVersion) {
         let t = AggregationJobTest::new(TEST_VDAF, HpkeKemId::X25519HkdfSha256, version);
         let reports = vec![
-            t.produce_invalid_report_public_share_decode_failure(DapMeasurement::U64(1), version),
-            t.produce_invalid_report_input_share_decode_failure(DapMeasurement::U64(1), version),
+            t.produce_invalid_report_public_share_decode_failure(
+                DapMeasurement::U32Vec(vec![1; 10]),
+                version,
+            ),
+            t.produce_invalid_report_input_share_decode_failure(
+                DapMeasurement::U32Vec(vec![1; 10]),
+                version,
+            ),
         ];
 
         let (agg_job_state, _agg_job_init_req) =
@@ -478,7 +367,7 @@ mod test {
 
     fn handle_agg_job_req_hpke_decrypt_err(version: DapVersion) {
         let t = AggregationJobTest::new(TEST_VDAF, HpkeKemId::X25519HkdfSha256, version);
-        let mut reports = t.produce_reports(vec![DapMeasurement::U64(1)]);
+        let mut reports = t.produce_reports(vec![DapMeasurement::U32Vec(vec![1; 10])]);
 
         // Simulate HPKE decryption error of helper's report share.
         reports[0].encrypted_input_shares[1].payload[0] ^= 1;
@@ -505,7 +394,7 @@ mod test {
                 &t.client_hpke_config_list,
                 t.valid_report_time_range().start - 1,
                 &t.task_id,
-                DapMeasurement::U64(1),
+                DapMeasurement::U32Vec(vec![1; 10]),
                 t.task_config.version,
             )
             .unwrap()];
@@ -540,7 +429,7 @@ mod test {
                 &t.client_hpke_config_list,
                 t.valid_report_time_range().end + 1,
                 &t.task_id,
-                DapMeasurement::U64(1),
+                DapMeasurement::U32Vec(vec![1; 10]),
                 t.task_config.version,
             )
             .unwrap()];
@@ -568,7 +457,7 @@ mod test {
 
     fn handle_agg_job_req_hpke_unknown_config_id(version: DapVersion) {
         let t = AggregationJobTest::new(TEST_VDAF, HpkeKemId::X25519HkdfSha256, version);
-        let mut reports = t.produce_reports(vec![DapMeasurement::U64(1)]);
+        let mut reports = t.produce_reports(vec![DapMeasurement::U32Vec(vec![1; 10])]);
 
         // Client tries to send Helper encrypted input with incorrect config ID.
         reports[0].encrypted_input_shares[1].config_id ^= 1;
@@ -588,10 +477,14 @@ mod test {
 
     fn handle_agg_job_req_vdaf_prep_error(version: DapVersion) {
         let t = AggregationJobTest::new(TEST_VDAF, HpkeKemId::X25519HkdfSha256, version);
-        let report0 =
-            t.produce_invalid_report_public_share_decode_failure(DapMeasurement::U64(1), version);
-        let report1 =
-            t.produce_invalid_report_input_share_decode_failure(DapMeasurement::U64(1), version);
+        let report0 = t.produce_invalid_report_public_share_decode_failure(
+            DapMeasurement::U32Vec(vec![1; 10]),
+            version,
+        );
+        let report1 = t.produce_invalid_report_input_share_decode_failure(
+            DapMeasurement::U32Vec(vec![1; 10]),
+            version,
+        );
 
         let agg_job_init_req = AggregationJobInitReq {
             agg_param: Vec::new(),
@@ -633,7 +526,10 @@ mod test {
 
     fn agg_job_resp_abort_transition_out_of_order(version: DapVersion) {
         let t = AggregationJobTest::new(TEST_VDAF, HpkeKemId::X25519HkdfSha256, version);
-        let reports = t.produce_reports(vec![DapMeasurement::U64(1), DapMeasurement::U64(1)]);
+        let reports = t.produce_reports(vec![
+            DapMeasurement::U32Vec(vec![1; 10]),
+            DapMeasurement::U32Vec(vec![1; 10]),
+        ]);
         let (leader_state, agg_job_init_req) =
             t.produce_agg_job_req(&DapAggregationParam::Empty, reports);
         let (_agg_span, mut agg_job_resp) = t.handle_agg_job_req(agg_job_init_req);
@@ -653,7 +549,10 @@ mod test {
 
     fn agg_job_resp_abort_report_id_repeated(version: DapVersion) {
         let t = AggregationJobTest::new(TEST_VDAF, HpkeKemId::X25519HkdfSha256, version);
-        let reports = t.produce_reports(vec![DapMeasurement::U64(1), DapMeasurement::U64(1)]);
+        let reports = t.produce_reports(vec![
+            DapMeasurement::U32Vec(vec![1; 10]),
+            DapMeasurement::U32Vec(vec![1; 10]),
+        ]);
         let (leader_state, agg_job_init_req) =
             t.produce_agg_job_req(&DapAggregationParam::Empty, reports);
         let (_agg_span, mut agg_job_resp) = t.handle_agg_job_req(agg_job_init_req);
@@ -673,7 +572,10 @@ mod test {
     fn agg_job_resp_abort_unrecognized_report_id(version: DapVersion) {
         let mut rng = thread_rng();
         let t = AggregationJobTest::new(TEST_VDAF, HpkeKemId::X25519HkdfSha256, version);
-        let reports = t.produce_reports(vec![DapMeasurement::U64(1), DapMeasurement::U64(1)]);
+        let reports = t.produce_reports(vec![
+            DapMeasurement::U32Vec(vec![1; 10]),
+            DapMeasurement::U32Vec(vec![1; 10]),
+        ]);
         let (leader_state, agg_job_init_req) =
             t.produce_agg_job_req(&DapAggregationParam::Empty, reports);
         let (_agg_span, mut agg_job_resp) = t.handle_agg_job_req(agg_job_init_req);
@@ -694,7 +596,7 @@ mod test {
 
     fn agg_job_resp_abort_invalid_transition(version: DapVersion) {
         let t = AggregationJobTest::new(TEST_VDAF, HpkeKemId::X25519HkdfSha256, version);
-        let reports = t.produce_reports(vec![DapMeasurement::U64(1)]);
+        let reports = t.produce_reports(vec![DapMeasurement::U32Vec(vec![1; 10])]);
         let (leader_state, agg_job_init_req) =
             t.produce_agg_job_req(&DapAggregationParam::Empty, reports);
         let (_helper_agg_span, mut agg_job_resp) = t.handle_agg_job_req(agg_job_init_req);
@@ -711,59 +613,14 @@ mod test {
 
     test_versions! { agg_job_resp_abort_invalid_transition }
 
-    #[test]
-    fn finish_agg_job_vdaf_draft09() {
-        let version = DapVersion::Draft09;
-        let t = AggregationJobTest::new(TEST_VDAF_DRAFT09, HpkeKemId::X25519HkdfSha256, version);
-        let reports = t.produce_reports(vec![
-            DapMeasurement::U64(1),
-            DapMeasurement::U64(1),
-            DapMeasurement::U64(0),
-            DapMeasurement::U64(0),
-            DapMeasurement::U64(1),
-        ]);
-
-        let (leader_state, agg_job_init_req) =
-            t.produce_agg_job_req(&DapAggregationParam::Empty, reports);
-
-        let (leader_agg_span, helper_agg_span) = {
-            let (helper_agg_span, agg_job_resp) = t.handle_agg_job_req(agg_job_init_req);
-            let leader_agg_span = t.consume_agg_job_resp(leader_state, agg_job_resp);
-
-            (leader_agg_span, helper_agg_span)
-        };
-
-        assert_eq!(leader_agg_span.report_count(), 5);
-        let num_measurements = leader_agg_span.report_count();
-
-        let VdafAggregateShare::Field64Draft09(leader_agg_share) =
-            leader_agg_span.collapsed().data.unwrap()
-        else {
-            panic!("unexpected VdafAggregateShare variant")
-        };
-
-        let VdafAggregateShare::Field64Draft09(helper_agg_share) =
-            helper_agg_span.collapsed().data.unwrap()
-        else {
-            panic!("unexpected VdafAggregateShare variant")
-        };
-
-        let vdaf = Prio3Draft09::new_count(2).unwrap();
-        assert_eq!(
-            vdaf.unshard(&(), [leader_agg_share, helper_agg_share], num_measurements,)
-                .unwrap(),
-            3,
-        );
-    }
-
     fn finish_agg_job(version: DapVersion) {
         let t = AggregationJobTest::new(TEST_VDAF, HpkeKemId::X25519HkdfSha256, version);
         let reports = t.produce_reports(vec![
-            DapMeasurement::U64(1),
-            DapMeasurement::U64(1),
-            DapMeasurement::U64(0),
-            DapMeasurement::U64(0),
-            DapMeasurement::U64(1),
+            DapMeasurement::U32Vec(vec![1; 10]),
+            DapMeasurement::U32Vec(vec![1; 10]),
+            DapMeasurement::U32Vec(vec![0; 10]),
+            DapMeasurement::U32Vec(vec![0; 10]),
+            DapMeasurement::U32Vec(vec![1; 10]),
         ]);
 
         let (leader_state, agg_job_init_req) =
@@ -779,36 +636,40 @@ mod test {
         assert_eq!(leader_agg_span.report_count(), 5);
         let num_measurements = leader_agg_span.report_count();
 
-        let VdafAggregateShare::Field64(leader_agg_share) =
+        let VdafAggregateShare::Field32(leader_agg_share) =
             leader_agg_span.collapsed().data.unwrap()
         else {
             panic!("unexpected VdafAggregateShare variant")
         };
 
-        let VdafAggregateShare::Field64(helper_agg_share) =
+        let VdafAggregateShare::Field32(helper_agg_share) =
             helper_agg_span.collapsed().data.unwrap()
         else {
             panic!("unexpected VdafAggregateShare variant")
         };
 
-        let vdaf = Prio3::new_count(2).unwrap();
+        let vdaf = Prio2::new(10).unwrap();
         assert_eq!(
             vdaf.unshard(&(), [leader_agg_share, helper_agg_share], num_measurements,)
                 .unwrap(),
-            3,
+            vec![3; 10],
         );
     }
 
     test_versions! { finish_agg_job }
 
-    #[tokio::test]
-    async fn agg_job_init_req_skip_vdaf_prep_error_draft09() {
-        let t =
-            AggregationJobTest::new(TEST_VDAF, HpkeKemId::X25519HkdfSha256, DapVersion::Draft09);
-        let mut reports = t.produce_reports(vec![DapMeasurement::U64(1), DapMeasurement::U64(1)]);
+    fn agg_job_init_req_skip_vdaf_prep_error(version: DapVersion) {
+        let t = AggregationJobTest::new(TEST_VDAF, HpkeKemId::X25519HkdfSha256, version);
+        let mut reports = t.produce_reports(vec![
+            DapMeasurement::U32Vec(vec![1; 10]),
+            DapMeasurement::U32Vec(vec![1; 10]),
+        ]);
         reports.insert(
             1,
-            t.produce_invalid_report_vdaf_prep_failure(DapMeasurement::U64(1), DapVersion::Draft09),
+            t.produce_invalid_report_vdaf_prep_failure(
+                DapMeasurement::U32Vec(vec![1; 10]),
+                version,
+            ),
         );
 
         let (leader_state, agg_job_init_req) =
@@ -830,6 +691,8 @@ mod test {
         assert_eq!(leader_agg_span.report_count(), 2);
     }
 
+    test_versions! { agg_job_init_req_skip_vdaf_prep_error }
+
     fn encrypted_agg_share(version: DapVersion) {
         let t = AggregationJobTest::new(TEST_VDAF, HpkeKemId::X25519HkdfSha256, version);
         let leader_agg_share = DapAggregateShare {
@@ -837,22 +700,18 @@ mod test {
             min_time: 1_637_359_200,
             max_time: 1_637_359_200,
             checksum: [0; 32],
-            data: Some(VdafAggregateShare::Field64Draft09(
-                AggregateShareDraft09::from(OutputShareDraft09::from(vec![Field64Draft09::from(
-                    23,
-                )])),
-            )),
+            data: Some(VdafAggregateShare::Field32(AggregateShare::from(
+                OutputShare::from(vec![FieldPrio2::from(23); 10]),
+            ))),
         };
         let helper_agg_share = DapAggregateShare {
             report_count: 50,
             min_time: 1_637_359_200,
             max_time: 1_637_359_200,
             checksum: [0; 32],
-            data: Some(VdafAggregateShare::Field64Draft09(
-                AggregateShareDraft09::from(OutputShareDraft09::from(vec![Field64Draft09::from(
-                    9,
-                )])),
-            )),
+            data: Some(VdafAggregateShare::Field32(AggregateShare::from(
+                OutputShare::from(vec![FieldPrio2::from(9); 10]),
+            ))),
         };
 
         let batch_selector = BatchSelector::TimeInterval {
@@ -878,7 +737,7 @@ mod test {
             vec![leader_encrypted_agg_share, helper_encrypted_agg_share],
         );
 
-        assert_eq!(agg_res, DapAggregateResult::U64(32));
+        assert_eq!(agg_res, DapAggregateResult::U32Vec(vec![32; 10]));
     }
 
     test_versions! { encrypted_agg_share }
@@ -892,7 +751,7 @@ mod test {
                 &t.client_hpke_config_list,
                 t.now,
                 &t.task_id,
-                DapMeasurement::U64(1),
+                DapMeasurement::U32Vec(vec![1; 10]),
                 vec![Extension::NotImplemented {
                     typ: 0xffff,
                     payload: b"some extension data".to_vec(),
@@ -934,7 +793,7 @@ mod test {
                 &t.client_hpke_config_list,
                 t.now,
                 &t.task_id,
-                DapMeasurement::U64(1),
+                DapMeasurement::U32Vec(vec![1; 10]),
                 vec![
                     Extension::NotImplemented {
                         typ: 23,
@@ -982,7 +841,12 @@ mod test {
             let (invalid_public_share, mut invalid_input_shares) = self
                 .task_config
                 .vdaf
-                .produce_input_shares(measurement, &report_id.0, &self.task_id)
+                .produce_input_shares(
+                    measurement,
+                    &report_id.0,
+                    &self.task_id,
+                    self.task_config.version,
+                )
                 .unwrap();
             invalid_input_shares[1][0] ^= 1; // The first bit is incorrect!
             VdafConfig::produce_report_with_extensions_for_shares(
@@ -1008,7 +872,12 @@ mod test {
             let (mut invalid_public_share, invalid_input_shares) = self
                 .task_config
                 .vdaf
-                .produce_input_shares(measurement, &report_id.0, &self.task_id)
+                .produce_input_shares(
+                    measurement,
+                    &report_id.0,
+                    &self.task_id,
+                    self.task_config.version,
+                )
                 .unwrap();
             invalid_public_share.push(1); // Add spurious byte at the end
             VdafConfig::produce_report_with_extensions_for_shares(
@@ -1034,7 +903,12 @@ mod test {
             let (invalid_public_share, mut invalid_input_shares) = self
                 .task_config
                 .vdaf
-                .produce_input_shares(measurement, &report_id.0, &self.task_id)
+                .produce_input_shares(
+                    measurement,
+                    &report_id.0,
+                    &self.task_id,
+                    self.task_config.version,
+                )
                 .unwrap();
             invalid_input_shares[0].push(1); // Add a spurious byte to the Leader's share
             invalid_input_shares[1].push(1); // Add a spurious byte to the Helper's share
diff --git a/crates/daphne/src/protocol/report_init.rs b/crates/daphne/src/protocol/report_init.rs
index 2749840be..0d1b88001 100644
--- a/crates/daphne/src/protocol/report_init.rs
+++ b/crates/daphne/src/protocol/report_init.rs
@@ -10,10 +10,7 @@ use crate::{
         self, Extension, PlaintextInputShare, ReportError, ReportMetadata, ReportShare, TaskId,
     },
     protocol::{decode_ping_pong_framed, no_duplicates, PingPongMessageType},
-    vdaf::{
-        prio2::prio2_prep_init, prio3::prio3_prep_init, prio3_draft09::prio3_draft09_prep_init,
-        VdafConfig, VdafPrepShare, VdafPrepState,
-    },
+    vdaf::{prio2::prio2_prep_init, VdafConfig, VdafPrepShare, VdafPrepState},
     DapAggregationParam, DapError, DapTaskConfig,
 };
 use prio::codec::{CodecError, ParameterizedDecode as _};
@@ -197,16 +194,8 @@ impl<P> InitializedReport<P> {
             DapAggregatorRole::Helper => 1,
         };
         let res = match &task_config.vdaf {
-            VdafConfig::Prio3Draft09(ref prio3_config) => prio3_draft09_prep_init(
-                prio3_config,
-                &task_config.vdaf_verify_key,
-                agg_id,
-                &report_share.report_metadata.id.0,
-                &report_share.public_share,
-                &input_share,
-            ),
-            VdafConfig::Prio3(ref prio3_config) => prio3_prep_init(
-                prio3_config,
+            VdafConfig::Prio3(prio3_config) => prio3_config.prep_init(
+                task_config.version,
                 &task_config.vdaf_verify_key,
                 *task_id,
                 agg_id,
diff --git a/crates/daphne/src/roles/helper.rs b/crates/daphne/src/roles/helper.rs
index 39f9998f1..2d4e3b13a 100644
--- a/crates/daphne/src/roles/helper.rs
+++ b/crates/daphne/src/roles/helper.rs
@@ -232,6 +232,7 @@ async fn finish_agg_job_and_aggregate(
             &report_status,
             part_batch_sel,
             initialized_reports,
+            task_config.version,
         )?;
 
         let put_shares_result = helper
diff --git a/crates/daphne/src/roles/leader/mod.rs b/crates/daphne/src/roles/leader/mod.rs
index 503461805..a1fb09378 100644
--- a/crates/daphne/src/roles/leader/mod.rs
+++ b/crates/daphne/src/roles/leader/mod.rs
@@ -341,8 +341,13 @@ async fn run_agg_job<A: DapLeader>(
             .map_err(|e| DapAbort::from_codec_error(e, *task_id))?;
 
     // Handle AggregationJobResp.
-    let agg_span =
-        task_config.consume_agg_job_resp(task_id, agg_job_state, agg_job_resp, metrics)?;
+    let agg_span = task_config.consume_agg_job_resp(
+        task_id,
+        agg_job_state,
+        agg_job_resp,
+        metrics,
+        task_config.version,
+    )?;
 
     let out_shares_count = agg_span.report_count() as u64;
     if out_shares_count == 0 {
diff --git a/crates/daphne/src/roles/mod.rs b/crates/daphne/src/roles/mod.rs
index 1b038be73..0754a9a61 100644
--- a/crates/daphne/src/roles/mod.rs
+++ b/crates/daphne/src/roles/mod.rs
@@ -198,7 +198,9 @@ mod test {
             };
 
             // Task Parameters that the Leader and Helper must agree on.
-            let vdaf_config = VdafConfig::Prio3(Prio3Config::Count);
+            //
+            // We need to use a VDAF that is compatible with all versions of DAP.
+            let vdaf_config = VdafConfig::Prio2 { dimension: 10 };
             let leader_url = Url::parse("https://leader.com/v02/").unwrap();
             let helper_url = Url::parse("http://helper.org:8788/v02/").unwrap();
             let collector_hpke_receiver_config =
@@ -483,12 +485,12 @@ mod test {
         }
 
         pub async fn gen_test_report(&self, task_id: &TaskId) -> Report {
-            // Construct report. We expect the VDAF to be Prio3Count so that we know what type of
-            // measurement to generate. However, we could extend the code to support more VDAFs.
+            // Construct report. We expect the VDAF to be Prio2 because it's supported in all
+            // versions of DAP. In the future we might want to test multiple different VDAFs.
             let task_config = self.leader.unchecked_get_task_config(task_id).await;
-            assert_matches!(task_config.vdaf, VdafConfig::Prio3(Prio3Config::Count));
+            assert_matches!(task_config.vdaf, VdafConfig::Prio2 { dimension: 10 });
 
-            self.gen_test_report_for_measurement(task_id, DapMeasurement::U64(1))
+            self.gen_test_report_for_measurement(task_id, DapMeasurement::U32Vec(vec![1; 10]))
                 .await
         }
 
@@ -1524,28 +1526,28 @@ mod test {
 
     async_test_versions! { e2e_taskprov_prio2 }
 
-    async fn e2e_taskprov_prio3_draft09_sum_vec_field64_multiproof_hmac_sha256_aes128(
-        version: DapVersion,
-    ) {
+    #[tokio::test]
+    async fn e2e_taskprov_prio3_draft09_sum_vec_field64_multiproof_hmac_sha256_aes128_draft09() {
         e2e_taskprov(
-            version,
-            VdafConfig::Prio3Draft09(Prio3Config::SumVecField64MultiproofHmacSha256Aes128 {
-                bits: 1,
-                length: 10,
-                chunk_length: 2,
-                num_proofs: 3,
-            }),
+            DapVersion::Draft09,
+            VdafConfig::Prio3(
+                Prio3Config::Draft09SumVecField64MultiproofHmacSha256Aes128 {
+                    bits: 1,
+                    length: 10,
+                    chunk_length: 2,
+                    num_proofs: 3,
+                },
+            ),
             DapMeasurement::U64Vec(vec![1; 10]),
         )
         .await;
     }
 
-    async_test_versions! { e2e_taskprov_prio3_draft09_sum_vec_field64_multiproof_hmac_sha256_aes128 }
-
-    async fn e2e_taskprov_pine32_hmac_sha256_aes128(version: DapVersion) {
+    #[tokio::test]
+    async fn e2e_taskprov_pine32_hmac_sha256_aes128_draft09() {
         use crate::{pine::PineParam, vdaf::pine::PineConfig};
         e2e_taskprov(
-            version,
+            DapVersion::Draft09,
             VdafConfig::Pine(PineConfig::Field32HmacSha256Aes128 {
                 param: PineParam {
                     norm_bound: 16,
@@ -1564,12 +1566,11 @@ mod test {
         .await;
     }
 
-    async_test_versions! { e2e_taskprov_pine32_hmac_sha256_aes128 }
-
-    async fn e2e_taskprov_pine64_hmac_sha256_aes128(version: DapVersion) {
+    #[tokio::test]
+    async fn e2e_taskprov_pine64_hmac_sha256_aes128_draft09() {
         use crate::{pine::PineParam, vdaf::pine::PineConfig};
         e2e_taskprov(
-            version,
+            DapVersion::Draft09,
             VdafConfig::Pine(PineConfig::Field64HmacSha256Aes128 {
                 param: PineParam {
                     norm_bound: 16,
@@ -1588,8 +1589,6 @@ mod test {
         .await;
     }
 
-    async_test_versions! { e2e_taskprov_pine64_hmac_sha256_aes128 }
-
     // Test multiple tasks in flight at once.
     async fn multi_task(version: DapVersion) {
         let t = Test::new(version);
diff --git a/crates/daphne/src/taskprov.rs b/crates/daphne/src/taskprov.rs
index 666dab673..ab96273c5 100644
--- a/crates/daphne/src/taskprov.rs
+++ b/crates/daphne/src/taskprov.rs
@@ -181,7 +181,7 @@ impl VdafConfig {
                 })?,
             }),
             (
-                DapVersion::Draft09 | DapVersion::Latest,
+                DapVersion::Draft09,
                 VdafTypeVar::Prio3SumVecField64MultiproofHmacSha256Aes128 {
                     bits,
                     length,
@@ -197,8 +197,8 @@ impl VdafConfig {
                         task_id: *task_id,
                     });
                 }
-                Ok(VdafConfig::Prio3Draft09(
-                    Prio3Config::SumVecField64MultiproofHmacSha256Aes128 {
+                Ok(VdafConfig::Prio3(
+                    Prio3Config::Draft09SumVecField64MultiproofHmacSha256Aes128 {
                         bits: bits.into(),
                         length: length.try_into().map_err(|_| DapAbort::InvalidTask {
                             detail: "length is larger than the system's word size".to_string(),
@@ -215,7 +215,7 @@ impl VdafConfig {
                     },
                 ))
             }
-            (_, VdafTypeVar::Pine32HmacSha256Aes128 { param }) => {
+            (DapVersion::Draft09, VdafTypeVar::Pine32HmacSha256Aes128 { param }) => {
                 if let Err(e) = pine32_hmac_sha256_aes128(&param) {
                     Err(DapAbort::InvalidTask {
                         detail: format!("invalid parameters for Pine32: {e}"),
@@ -232,7 +232,7 @@ impl VdafConfig {
                     }))
                 }
             }
-            (_, VdafTypeVar::Pine64HmacSha256Aes128 { param }) => {
+            (DapVersion::Draft09, VdafTypeVar::Pine64HmacSha256Aes128 { param }) => {
                 if let Err(e) = pine64_hmac_sha256_aes128(&param) {
                     Err(DapAbort::InvalidTask {
                         detail: format!("invalid parameters for Pine64: {e}"),
@@ -253,6 +253,10 @@ impl VdafConfig {
                 detail: format!("unimplemented VDAF type ({typ})"),
                 task_id: *task_id,
             }),
+            (_, _) => Err(DapAbort::InvalidTask {
+                detail: format!("VDAF not supported in {version}"),
+                task_id: *task_id,
+            }),
         }
     }
 }
@@ -380,7 +384,7 @@ impl TryFrom<&VdafConfig> for messages::taskprov::VdafTypeVar {
                     fatal_error!(err = "{vdaf_config}: dimension is too large for taskprov")
                 })?,
             }),
-            VdafConfig::Prio3Draft09(Prio3Config::SumVecField64MultiproofHmacSha256Aes128 {
+            VdafConfig::Prio3(Prio3Config::Draft09SumVecField64MultiproofHmacSha256Aes128 {
                 bits,
                 length,
                 chunk_length,
@@ -398,9 +402,6 @@ impl TryFrom<&VdafConfig> for messages::taskprov::VdafTypeVar {
                 })?,
                 num_proofs: *num_proofs,
             }),
-            VdafConfig::Prio3Draft09(..) => Err(fatal_error!(
-                err = format!("{vdaf_config} is not currently supported for taskprov")
-            )),
             VdafConfig::Prio3(..) => Err(fatal_error!(
                 err = format!("{vdaf_config} is not currently supported for taskprov")
             )),
diff --git a/crates/daphne/src/testing/mod.rs b/crates/daphne/src/testing/mod.rs
index 16e49e337..5b32c3044 100644
--- a/crates/daphne/src/testing/mod.rs
+++ b/crates/daphne/src/testing/mod.rs
@@ -223,6 +223,7 @@ impl AggregationJobTest {
                         self.replay_protection,
                     )
                     .unwrap(),
+                self.task_config.version,
             )
             .unwrap()
     }
@@ -241,6 +242,7 @@ impl AggregationJobTest {
                 leader_state,
                 agg_job_resp,
                 &self.leader_metrics,
+                self.task_config.version,
             )
             .unwrap()
     }
@@ -253,7 +255,13 @@ impl AggregationJobTest {
     ) -> DapError {
         let metrics = &self.leader_metrics;
         self.task_config
-            .consume_agg_job_resp(&self.task_id, leader_state, agg_job_resp, metrics)
+            .consume_agg_job_resp(
+                &self.task_id,
+                leader_state,
+                agg_job_resp,
+                metrics,
+                self.task_config.version,
+            )
             .expect_err("consume_agg_job_resp() succeeded; expected failure")
     }
 
@@ -1113,9 +1121,10 @@ impl VdafConfig {
     pub fn gen_measurement(&self) -> Result<DapMeasurement, DapError> {
         match self {
             Self::Prio2 { dimension } => Ok(DapMeasurement::U32Vec(vec![1; *dimension])),
-            Self::Prio3Draft09(
-                crate::vdaf::Prio3Config::SumVecField64MultiproofHmacSha256Aes128 {
-                    length, ..
+            Self::Prio3(
+                crate::vdaf::Prio3Config::Draft09SumVecField64MultiproofHmacSha256Aes128 {
+                    length,
+                    ..
                 },
             ) => Ok(DapMeasurement::U64Vec(vec![0; *length])),
             _ => Err(fatal_error!(
diff --git a/crates/daphne/src/vdaf/mod.rs b/crates/daphne/src/vdaf/mod.rs
index d3eabf1e5..9c95f53d7 100644
--- a/crates/daphne/src/vdaf/mod.rs
+++ b/crates/daphne/src/vdaf/mod.rs
@@ -74,7 +74,6 @@ pub(crate) enum VdafError {
 #[serde(rename_all = "snake_case")]
 #[cfg_attr(any(test, feature = "test-utils"), derive(deepsize::DeepSizeOf))]
 pub enum VdafConfig {
-    Prio3Draft09(Prio3Config),
     Prio3(Prio3Config),
     Prio2 {
         dimension: usize,
@@ -112,7 +111,6 @@ pub(crate) fn from_codec_error(c: CodecErrorDraft09) -> CodecError {
 impl std::fmt::Display for VdafConfig {
     fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result {
         match self {
-            VdafConfig::Prio3Draft09(prio3_config) => write!(f, "Prio3Draft09({prio3_config})"),
             VdafConfig::Prio3(prio3_config) => write!(f, "Prio3({prio3_config})"),
             VdafConfig::Prio2 { dimension } => write!(f, "Prio2({dimension})"),
             #[cfg(feature = "experimental")]
@@ -135,8 +133,8 @@ pub enum Prio3Config {
     Count,
 
     /// The sum of 64-bit, unsigned integers. Each measurement is an integer in range `[0,
-    /// 2^bits)`.
-    Sum { bits: usize },
+    /// max_measurement]`.
+    Sum { max_measurement: u64 },
 
     /// A histogram for estimating the distribution of 64-bit, unsigned integers where each
     /// measurement is a bucket index in range `[0, len)`.
@@ -151,8 +149,11 @@ pub enum Prio3Config {
     },
 
     /// A variant of `SumVec` that uses a smaller field (`Field64`), multiple proofs, and a custom
-    /// XOF (`XofHmacSha256Aes128`).
-    SumVecField64MultiproofHmacSha256Aes128 {
+    /// XOF (`XofHmacSha256Aes128`). This VDAF is only supported in DAP-09.
+    //
+    // Ensure the serialization of this type is backwards compatible.
+    #[serde(rename = "sum_vec_field64_multiproof_hmac_sha256_aes128")]
+    Draft09SumVecField64MultiproofHmacSha256Aes128 {
         bits: usize,
         length: usize,
         chunk_length: usize,
@@ -168,18 +169,18 @@ impl std::fmt::Display for Prio3Config {
                 length,
                 chunk_length,
             } => write!(f, "Histogram({length},{chunk_length})"),
-            Prio3Config::Sum { bits } => write!(f, "Sum({bits})"),
+            Prio3Config::Sum { max_measurement } => write!(f, "Sum({max_measurement})"),
             Prio3Config::SumVec {
                 bits,
                 length,
                 chunk_length,
             } => write!(f, "SumVec({bits},{length},{chunk_length})"),
-            Prio3Config::SumVecField64MultiproofHmacSha256Aes128 {
+            Prio3Config::Draft09SumVecField64MultiproofHmacSha256Aes128 {
                 bits,
                 length,
                 chunk_length,
                 num_proofs,
-            } => write!(f, "SumVecField64MultiproofHmacSha256Aes128({bits},{length},{chunk_length},{num_proofs})"),
+            } => write!(f, "Draft09SumVecField64MultiproofHmacSha256Aes128({bits},{length},{chunk_length},{num_proofs})"),
         }
     }
 }
@@ -231,9 +232,7 @@ impl AsMut<[u8]> for VdafVerifyKey {
 #[cfg_attr(any(test, feature = "test-utils"), derive(Debug, Eq, PartialEq))]
 pub enum VdafPrepState {
     Prio2(Prio2PrepareState),
-    Prio3Draft09Field64(Prio3Draft09PrepareState<Field64Draft09, 16>),
     Prio3Draft09Field64HmacSha256Aes128(Prio3Draft09PrepareState<Field64Draft09, 32>),
-    Prio3Draft09Field128(Prio3Draft09PrepareState<Field128Draft09, 16>),
     Prio3Field64(Prio3PrepareState<Field64, 32>),
     Prio3Field64HmacSha256Aes128(Prio3PrepareState<Field64, 32>),
     Prio3Field128(Prio3PrepareState<Field128, 32>),
@@ -254,9 +253,7 @@ impl deepsize::DeepSizeOf for VdafPrepState {
         // This happens to be correct for helpers but not for leaders
         match self {
             Self::Prio2(_)
-            | Self::Prio3Draft09Field64(_)
             | Self::Prio3Draft09Field64HmacSha256Aes128(_)
-            | Self::Prio3Draft09Field128(_)
             | Self::Prio3Field64(_)
             | Self::Prio3Field64HmacSha256Aes128(_)
             | Self::Prio3Field128(_)
@@ -273,10 +270,7 @@ impl deepsize::DeepSizeOf for VdafPrepState {
 #[cfg_attr(any(test, feature = "test-utils"), derive(Debug))]
 pub enum VdafPrepShare {
     Prio2(Prio2PrepareShare),
-    Prio3Draft09Field64(Prio3Draft09PrepareShare<Field64Draft09, 16>),
     Prio3Draft09Field64HmacSha256Aes128(Prio3Draft09PrepareShare<Field64Draft09, 32>),
-    Prio3Draft09Field128(Prio3Draft09PrepareShare<Field128Draft09, 16>),
-
     Prio3Field64(Prio3PrepareShare<Field64, 32>),
     Prio3Field64HmacSha256Aes128(Prio3PrepareShare<Field64, 32>),
     Prio3Field128(Prio3PrepareShare<Field128, 32>),
@@ -297,9 +291,7 @@ impl deepsize::DeepSizeOf for VdafPrepShare {
             // share. The length of the verifier share depends on the Prio3 type, which we don't
             // know at this point. Likewise, whether the XOF seed is present depends on the Prio3
             // type.
-            Self::Prio3Draft09Field64(..)
-            | Self::Prio3Draft09Field64HmacSha256Aes128(..)
-            | Self::Prio3Draft09Field128(..)
+            Self::Prio3Draft09Field64HmacSha256Aes128(..)
             | Self::Prio3Field64(..)
             | Self::Prio3Field64HmacSha256Aes128(..)
             | Self::Prio3Field128(..)
@@ -314,11 +306,9 @@ impl deepsize::DeepSizeOf for VdafPrepShare {
 impl Encode for VdafPrepShare {
     fn encode(&self, bytes: &mut Vec<u8>) -> Result<(), CodecError> {
         match self {
-            Self::Prio3Draft09Field64(share) => share.encode(bytes).map_err(from_codec_error),
             Self::Prio3Draft09Field64HmacSha256Aes128(share) => {
                 share.encode(bytes).map_err(from_codec_error)
             }
-            Self::Prio3Draft09Field128(share) => share.encode(bytes).map_err(from_codec_error),
             Self::Prio3Field64(share) => share.encode(bytes),
             Self::Prio3Field64HmacSha256Aes128(share) => share.encode(bytes),
             Self::Prio3Field128(share) => share.encode(bytes),
@@ -337,20 +327,12 @@ impl ParameterizedDecode<VdafPrepState> for VdafPrepShare {
         bytes: &mut std::io::Cursor<&[u8]>,
     ) -> Result<Self, CodecError> {
         match state {
-            VdafPrepState::Prio3Draft09Field64(state) => Ok(VdafPrepShare::Prio3Draft09Field64(
-                Prio3Draft09PrepareShare::decode_with_param(state, bytes)
-                    .map_err(from_codec_error)?,
-            )),
             VdafPrepState::Prio3Draft09Field64HmacSha256Aes128(state) => {
                 Ok(VdafPrepShare::Prio3Draft09Field64HmacSha256Aes128(
                     Prio3Draft09PrepareShare::decode_with_param(state, bytes)
                         .map_err(from_codec_error)?,
                 ))
             }
-            VdafPrepState::Prio3Draft09Field128(state) => Ok(VdafPrepShare::Prio3Draft09Field128(
-                Prio3Draft09PrepareShare::decode_with_param(state, bytes)
-                    .map_err(from_codec_error)?,
-            )),
             VdafPrepState::Prio3Field64(state) => Ok(VdafPrepShare::Prio3Field64(
                 Prio3PrepareShare::decode_with_param(state, bytes)?,
             )),
@@ -432,10 +414,7 @@ impl Encode for VdafAggregateShare {
 impl VdafConfig {
     pub(crate) fn uninitialized_verify_key(&self) -> VdafVerifyKey {
         match self {
-            Self::Prio3Draft09(Prio3Config::SumVecField64MultiproofHmacSha256Aes128 { .. })
-            | Self::Prio2 { .. }
-            | Self::Prio3(..) => VdafVerifyKey::L32([0; 32]),
-            Self::Prio3Draft09(..) => VdafVerifyKey::L16([0; 16]),
+            Self::Prio2 { .. } | Self::Prio3(..) => VdafVerifyKey::L32([0; 32]),
             #[cfg(feature = "experimental")]
             Self::Mastic { .. } => VdafVerifyKey::L16([0; 16]),
             Self::Pine(..) => VdafVerifyKey::L32([0; 32]),
@@ -445,18 +424,11 @@ impl VdafConfig {
     /// Parse a verification key from raw bytes.
     pub fn get_decoded_verify_key(&self, bytes: &[u8]) -> Result<VdafVerifyKey, CodecError> {
         match self {
-            Self::Prio3Draft09(Prio3Config::SumVecField64MultiproofHmacSha256Aes128 { .. })
-            | Self::Prio2 { .. }
-            | Self::Prio3(..) => Ok(VdafVerifyKey::L32(
+            Self::Prio2 { .. } | Self::Prio3(..) => Ok(VdafVerifyKey::L32(
                 <[u8; 32]>::try_from(bytes)
                     .map_err(|e| CodecErrorDraft09::Other(Box::new(e)))
                     .map_err(from_codec_error)?,
             )),
-            Self::Prio3Draft09(..) => Ok(VdafVerifyKey::L16(
-                <[u8; 16]>::try_from(bytes)
-                    .map_err(|e| CodecErrorDraft09::Other(Box::new(e)))
-                    .map_err(from_codec_error)?,
-            )),
             #[cfg(feature = "experimental")]
             Self::Mastic { .. } => Ok(VdafVerifyKey::L16(
                 <[u8; 16]>::try_from(bytes).map_err(|e| CodecError::Other(Box::new(e)))?,
@@ -481,7 +453,7 @@ impl VdafConfig {
     /// executed.
     pub fn is_valid_agg_param(&self, agg_param: &[u8]) -> bool {
         match self {
-            Self::Prio3Draft09(..) | Self::Prio3(..) | Self::Prio2 { .. } => agg_param.is_empty(),
+            Self::Prio3(..) | Self::Prio2 { .. } => agg_param.is_empty(),
             #[cfg(feature = "experimental")]
             Self::Mastic { .. } => true,
             Self::Pine(..) => agg_param.is_empty(),
@@ -612,7 +584,7 @@ where
     Ok(vdaf.unshard(&(), agg_shares_vec, num_measurements)?)
 }
 
-fn shard_then_encode_draft09<V: VdafDraft09 + ClientDraft09<16>>(
+pub(crate) fn shard_then_encode_draft09<V: VdafDraft09 + ClientDraft09<16>>(
     vdaf: &V,
     measurement: &V::Measurement,
     nonce: &[u8; 16],
diff --git a/crates/daphne/src/vdaf/prio3.rs b/crates/daphne/src/vdaf/prio3.rs
index 949ca61e3..35307d3a8 100644
--- a/crates/daphne/src/vdaf/prio3.rs
+++ b/crates/daphne/src/vdaf/prio3.rs
@@ -6,8 +6,8 @@
 use crate::{
     fatal_error,
     messages::TaskId,
-    vdaf::{VdafError, VdafVerifyKey},
-    DapAggregateResult, DapMeasurement, Prio3Config, VdafAggregateShare, VdafPrepShare,
+    vdaf::{prio3_draft09, VdafError, VdafVerifyKey},
+    DapAggregateResult, DapMeasurement, DapVersion, Prio3Config, VdafAggregateShare, VdafPrepShare,
     VdafPrepState,
 };
 
@@ -25,385 +25,542 @@ use prio::{
 
 const CTX_STRING_PREFIX: &[u8] = b"dap-13";
 
-/// Split the given measurement into a sequence of encoded input shares.
-pub(crate) fn prio3_shard(
-    config: &Prio3Config,
-    measurement: DapMeasurement,
-    nonce: &[u8; 16],
-    task_id: TaskId,
-) -> Result<(Vec<u8>, [Vec<u8>; 2]), VdafError> {
-    match (config, measurement) {
-        (Prio3Config::Count, DapMeasurement::U64(measurement)) if measurement < 2 => {
-            let vdaf = Prio3::new_count(2).map_err(|e| {
-                VdafError::Dap(
-                    fatal_error!(err = ?e, "failed to create prio3 count from num_aggregators(2)"),
-                )
-            })?;
-            shard_then_encode(&vdaf, task_id, &(measurement != 0), nonce)
-        }
-        (
-            Prio3Config::Histogram {
-                length,
-                chunk_length,
-            },
-            DapMeasurement::U64(measurement),
-        ) => {
-            let vdaf = Prio3::new_histogram(2, *length, *chunk_length)
-                .map_err(|e| VdafError::Dap(fatal_error!(err = ?e, "failed to create prio3 Histogram from num_aggregators(2), length({length}), chunk_length({chunk_length})")))?;
-            let m: usize = measurement.try_into().unwrap();
-            shard_then_encode(&vdaf, task_id, &m, nonce)
-        }
-        (Prio3Config::Sum { .. }, DapMeasurement::U64(_)) => {
-            Err(VdafError::Dap(fatal_error!(err = "Sum unimplemented")))
-        }
-        (
-            Prio3Config::SumVec {
-                bits,
-                length,
-                chunk_length,
-            },
-            DapMeasurement::U128Vec(measurement),
-        ) => {
-            let vdaf = Prio3::new_sum_vec(2, *bits, *length, *chunk_length)
-                .map_err(|e| VdafError::Dap(fatal_error!(err = ?e, "failed to create prio3 sum vec from num_aggregators(2), bits({bits}), length({length}), chunk_length({chunk_length})")))?;
-            shard_then_encode(&vdaf, task_id, &measurement, nonce)
+impl Prio3Config {
+    pub(crate) fn shard(
+        &self,
+        version: DapVersion,
+        measurement: DapMeasurement,
+        nonce: &[u8; 16],
+        task_id: TaskId,
+    ) -> Result<(Vec<u8>, [Vec<u8>; 2]), VdafError> {
+        match (version, self, measurement) {
+            (DapVersion::Latest, Prio3Config::Count, DapMeasurement::U64(measurement))
+                if measurement < 2 =>
+            {
+                let vdaf = Prio3::new_count(2).map_err(|e| {
+                    VdafError::Dap(fatal_error!(err = ?e, "initializing {self:?} failed"))
+                })?;
+                shard_then_encode(&vdaf, task_id, &(measurement != 0), nonce)
+            }
+            (
+                DapVersion::Latest,
+                Prio3Config::Sum { max_measurement },
+                DapMeasurement::U64(measurement),
+            ) => {
+                let vdaf = Prio3::new_sum(2, *max_measurement).map_err(|e| {
+                    VdafError::Dap(fatal_error!(err = ?e, "initializing {self:?} failed"))
+                })?;
+                shard_then_encode(&vdaf, task_id, &measurement, nonce)
+            }
+            (
+                DapVersion::Latest,
+                Prio3Config::Histogram {
+                    length,
+                    chunk_length,
+                },
+                DapMeasurement::U64(measurement),
+            ) => {
+                let vdaf = Prio3::new_histogram(2, *length, *chunk_length).map_err(|e| {
+                    VdafError::Dap(fatal_error!(err = ?e, "initializing {self:?} failed"))
+                })?;
+                let m: usize = measurement.try_into().unwrap();
+                shard_then_encode(&vdaf, task_id, &m, nonce)
+            }
+            (
+                DapVersion::Latest,
+                Prio3Config::SumVec {
+                    bits,
+                    length,
+                    chunk_length,
+                },
+                DapMeasurement::U128Vec(measurement),
+            ) => {
+                let vdaf = Prio3::new_sum_vec(2, *bits, *length, *chunk_length).map_err(|e| {
+                    VdafError::Dap(fatal_error!(err = ?e, "initializing {self:?} failed"))
+                })?;
+                shard_then_encode(&vdaf, task_id, &measurement, nonce)
+            }
+            (
+                DapVersion::Draft09,
+                Prio3Config::Draft09SumVecField64MultiproofHmacSha256Aes128 {
+                    bits,
+                    length,
+                    chunk_length,
+                    num_proofs,
+                },
+                DapMeasurement::U64Vec(measurement),
+            ) => {
+                let vdaf = prio3_draft09::new_prio3_sum_vec_field64_multiproof_hmac_sha256_aes128(
+                    *bits,
+                    *length,
+                    *chunk_length,
+                    *num_proofs,
+                )?;
+                super::shard_then_encode_draft09(&vdaf, &measurement, nonce)
+            }
+            _ => Err(VdafError::Dap(fatal_error!(
+                err =
+                    format!("unexpected measurement or {self:?} is not supported in DAP {version}")
+            ))),
         }
-        (
-            Prio3Config::SumVecField64MultiproofHmacSha256Aes128 { .. },
-            DapMeasurement::U64Vec(_),
-        ) => Err(VdafError::Dap(fatal_error!(
-            err = format!(
-                "prio3_shard: SumVecField64MultiproofHmacSha256Aes128 is not defined for VDAF-13"
-            )
-        ))),
-        _ => Err(VdafError::Dap(fatal_error!(
-            err = format!("prio3_shard: unexpected VDAF config {config:?}")
-        ))),
     }
-}
 
-/// Consume an input share and return the corresponding VDAF step and message.
-pub(crate) fn prio3_prep_init(
-    config: &Prio3Config,
-    verify_key: &VdafVerifyKey,
-    task_id: TaskId,
-    agg_id: usize,
-    nonce: &[u8; 16],
-    public_share_data: &[u8],
-    input_share_data: &[u8],
-) -> Result<(VdafPrepState, VdafPrepShare), VdafError> {
-    return match (&config, verify_key) {
-        (Prio3Config::Count, VdafVerifyKey::L32(verify_key)) => {
-            let vdaf = Prio3::new_count(2).map_err(|e| {
-                VdafError::Dap(
-                    fatal_error!(err = ?e, "failed to create prio3 from num_aggregators(2)"),
-                )
-            })?;
-            let (state, share) = prep_init(
-                vdaf,
-                task_id,
+    #[allow(clippy::too_many_arguments)]
+    pub(crate) fn prep_init(
+        &self,
+        version: DapVersion,
+        verify_key: &VdafVerifyKey,
+        task_id: TaskId,
+        agg_id: usize,
+        nonce: &[u8; 16],
+        public_share_data: &[u8],
+        input_share_data: &[u8],
+    ) -> Result<(VdafPrepState, VdafPrepShare), VdafError> {
+        return match (version, self, verify_key) {
+            (DapVersion::Latest, Prio3Config::Count, VdafVerifyKey::L32(verify_key)) => {
+                let vdaf = Prio3::new_count(2).map_err(|e| {
+                    VdafError::Dap(fatal_error!(err = ?e, "initializing {self:?} failed"))
+                })?;
+                let (state, share) = prep_init(
+                    vdaf,
+                    task_id,
+                    verify_key,
+                    agg_id,
+                    nonce,
+                    public_share_data,
+                    input_share_data,
+                )?;
+                Ok((
+                    VdafPrepState::Prio3Field64(state),
+                    VdafPrepShare::Prio3Field64(share),
+                ))
+            }
+            (
+                DapVersion::Latest,
+                Prio3Config::Sum { max_measurement },
+                VdafVerifyKey::L32(verify_key),
+            ) => {
+                let vdaf = Prio3::new_sum(2, *max_measurement).map_err(|e| {
+                    VdafError::Dap(fatal_error!(err = ?e, "initializing {self:?} failed"))
+                })?;
+                let (state, share) = prep_init(
+                    vdaf,
+                    task_id,
+                    verify_key,
+                    agg_id,
+                    nonce,
+                    public_share_data,
+                    input_share_data,
+                )?;
+                Ok((
+                    VdafPrepState::Prio3Field64(state),
+                    VdafPrepShare::Prio3Field64(share),
+                ))
+            }
+            (
+                DapVersion::Latest,
+                Prio3Config::Histogram {
+                    length,
+                    chunk_length,
+                },
+                VdafVerifyKey::L32(verify_key),
+            ) => {
+                let vdaf = Prio3::new_histogram(2, *length, *chunk_length).map_err(|e| {
+                    VdafError::Dap(fatal_error!(err = ?e, "initializing {self:?} failed"))
+                })?;
+                let (state, share) = prep_init(
+                    vdaf,
+                    task_id,
+                    verify_key,
+                    agg_id,
+                    nonce,
+                    public_share_data,
+                    input_share_data,
+                )?;
+                Ok((
+                    VdafPrepState::Prio3Field128(state),
+                    VdafPrepShare::Prio3Field128(share),
+                ))
+            }
+            (
+                DapVersion::Latest,
+                Prio3Config::SumVec {
+                    bits,
+                    length,
+                    chunk_length,
+                },
+                VdafVerifyKey::L32(verify_key),
+            ) => {
+                let vdaf = Prio3::new_sum_vec(2, *bits, *length, *chunk_length).map_err(|e| {
+                    VdafError::Dap(fatal_error!(err = ?e, "initializing {self:?} failed"))
+                })?;
+                let (state, share) = prep_init(
+                    vdaf,
+                    task_id,
+                    verify_key,
+                    agg_id,
+                    nonce,
+                    public_share_data,
+                    input_share_data,
+                )?;
+                Ok((
+                    VdafPrepState::Prio3Field128(state),
+                    VdafPrepShare::Prio3Field128(share),
+                ))
+            }
+            (
+                DapVersion::Draft09,
+                Prio3Config::Draft09SumVecField64MultiproofHmacSha256Aes128 {
+                    bits,
+                    length,
+                    chunk_length,
+                    num_proofs,
+                },
+                VdafVerifyKey::L32(verify_key),
+            ) => {
+                let vdaf = prio3_draft09::new_prio3_sum_vec_field64_multiproof_hmac_sha256_aes128(
+                    *bits,
+                    *length,
+                    *chunk_length,
+                    *num_proofs,
+                )?;
+                let (state, share) = prio3_draft09::prep_init_draft09(
+                    vdaf,
+                    verify_key,
+                    agg_id,
+                    nonce,
+                    public_share_data,
+                    input_share_data,
+                )?;
+                Ok((
+                    VdafPrepState::Prio3Draft09Field64HmacSha256Aes128(state),
+                    VdafPrepShare::Prio3Draft09Field64HmacSha256Aes128(share),
+                ))
+            }
+            _ => Err(VdafError::Dap(fatal_error!(
+                err =
+                    format!("unexpected verify key or {self:?} is not supported in DAP {version}")
+            ))),
+        };
+
+        type Prio3Prepared<T, const SEED_SIZE: usize> = (
+            Prio3PrepareState<<T as Type>::Field, SEED_SIZE>,
+            Prio3PrepareShare<<T as Type>::Field, SEED_SIZE>,
+        );
+
+        fn prep_init<T, P, const SEED_SIZE: usize>(
+            vdaf: Prio3<T, P, SEED_SIZE>,
+            task_id: TaskId,
+            verify_key: &[u8; SEED_SIZE],
+            agg_id: usize,
+            nonce: &[u8; 16],
+            public_share_data: &[u8],
+            input_share_data: &[u8],
+        ) -> Result<Prio3Prepared<T, SEED_SIZE>, VdafError>
+        where
+            T: Type,
+            P: Xof<SEED_SIZE>,
+        {
+            // Parse the public share.
+            let public_share = Prio3PublicShare::get_decoded_with_param(&vdaf, public_share_data)?;
+
+            // Parse the input share.
+            let input_share =
+                Prio3InputShare::get_decoded_with_param(&(&vdaf, agg_id), input_share_data)?;
+
+            let mut ctx = [0; CTX_STRING_PREFIX.len() + 32];
+            ctx[..CTX_STRING_PREFIX.len()].copy_from_slice(CTX_STRING_PREFIX);
+            ctx[CTX_STRING_PREFIX.len()..].copy_from_slice(&task_id.0);
+            // Run the prepare-init algorithm, returning the initial state.
+            Ok(vdaf.prepare_init(
                 verify_key,
+                &ctx,
                 agg_id,
+                &(),
                 nonce,
-                public_share_data,
-                input_share_data,
-            )?;
-            Ok((
+                &public_share,
+                &input_share,
+            )?)
+        }
+    }
+
+    pub(crate) fn prep_finish_from_shares(
+        &self,
+        version: DapVersion,
+        agg_id: usize,
+        task_id: TaskId,
+        host_state: VdafPrepState,
+        host_share: VdafPrepShare,
+        peer_share_data: &[u8],
+    ) -> Result<(VdafAggregateShare, Vec<u8>), VdafError> {
+        let (agg_share, outbound) = match (version, self, host_state, host_share) {
+            (
+                DapVersion::Latest,
+                Prio3Config::Count,
                 VdafPrepState::Prio3Field64(state),
                 VdafPrepShare::Prio3Field64(share),
-            ))
-        }
-        (
-            Prio3Config::Histogram {
-                length,
-                chunk_length,
-            },
-            VdafVerifyKey::L32(verify_key),
-        ) => {
-            let vdaf = Prio3::new_histogram(2, *length, *chunk_length)
-                .map_err(|e| VdafError::Dap(fatal_error!(err = ?e, "failed to create prio3 histogram from num_aggregators(2), length({length}), chunk_length({chunk_length})")))?;
-            let (state, share) = prep_init(
-                vdaf,
-                task_id,
-                verify_key,
-                agg_id,
-                nonce,
-                public_share_data,
-                input_share_data,
-            )?;
-            Ok((
+            ) => {
+                let vdaf = Prio3::new_count(2).map_err(|e| {
+                    VdafError::Dap(fatal_error!(err = ?e, "initializing {self:?} failed"))
+                })?;
+                let (out_share, outbound) =
+                    prep_finish_from_shares(&vdaf, task_id, agg_id, state, share, peer_share_data)?;
+                let agg_share = VdafAggregateShare::Field64(vdaf.aggregate(&(), [out_share])?);
+                (agg_share, outbound)
+            }
+            (
+                DapVersion::Latest,
+                Prio3Config::Sum { max_measurement },
+                VdafPrepState::Prio3Field64(state),
+                VdafPrepShare::Prio3Field64(share),
+            ) => {
+                let vdaf = Prio3::new_sum(2, *max_measurement).map_err(|e| {
+                    VdafError::Dap(fatal_error!(err = ?e, "initializing {self:?} failed"))
+                })?;
+                let (out_share, outbound) =
+                    prep_finish_from_shares(&vdaf, task_id, agg_id, state, share, peer_share_data)?;
+                let agg_share = VdafAggregateShare::Field64(vdaf.aggregate(&(), [out_share])?);
+                (agg_share, outbound)
+            }
+            (
+                DapVersion::Latest,
+                Prio3Config::Histogram {
+                    length,
+                    chunk_length,
+                },
                 VdafPrepState::Prio3Field128(state),
                 VdafPrepShare::Prio3Field128(share),
-            ))
-        }
-        (Prio3Config::Sum { .. }, VdafVerifyKey::L32(_)) => {
-            Err(VdafError::Dap(fatal_error!(err = "sum unimplemented")))
-        }
-        (
-            Prio3Config::SumVec {
-                bits,
-                length,
-                chunk_length,
-            },
-            VdafVerifyKey::L32(verify_key),
-        ) => {
-            let vdaf = Prio3::new_sum_vec(2, *bits, *length, *chunk_length)
-                .map_err(|e| VdafError::Dap(fatal_error!(err = ?e, "failed to create prio3 sum vec from num_aggregators(2), bits({bits}), length({length}), chunk_length({chunk_length})")))?;
-            let (state, share) = prep_init(
-                vdaf,
-                task_id,
-                verify_key,
-                agg_id,
-                nonce,
-                public_share_data,
-                input_share_data,
-            )?;
-            Ok((
+            ) => {
+                let vdaf = Prio3::new_histogram(2, *length, *chunk_length).map_err(|e| {
+                    VdafError::Dap(fatal_error!(err = ?e, "initializing {self:?} failed"))
+                })?;
+                let (out_share, outbound) =
+                    prep_finish_from_shares(&vdaf, task_id, agg_id, state, share, peer_share_data)?;
+                let agg_share = VdafAggregateShare::Field128(vdaf.aggregate(&(), [out_share])?);
+                (agg_share, outbound)
+            }
+            (
+                DapVersion::Latest,
+                Prio3Config::SumVec {
+                    bits,
+                    length,
+                    chunk_length,
+                },
                 VdafPrepState::Prio3Field128(state),
                 VdafPrepShare::Prio3Field128(share),
-            ))
-        }
-        (
-            Prio3Config::SumVecField64MultiproofHmacSha256Aes128 {
-            ..},
-            VdafVerifyKey::L32(_),
-        ) => {
-            Err(VdafError::Dap(fatal_error!(err = format!("prio3_shard: SumVecField64MultiproofHmacSha256Aes128 is not defined for VDAF-13"))))
-        },
-        _ => {
-            return Err(VdafError::Dap(fatal_error!(
-                err = "unhandled config and verify key combination",
-            )))
-        }
-
-    };
+            ) => {
+                let vdaf = Prio3::new_sum_vec(2, *bits, *length, *chunk_length).map_err(|e| {
+                    VdafError::Dap(fatal_error!(err = ?e, "initializing {self:?} failed"))
+                })?;
+                let (out_share, outbound) =
+                    prep_finish_from_shares(&vdaf, task_id, agg_id, state, share, peer_share_data)?;
+                let agg_share = VdafAggregateShare::Field128(vdaf.aggregate(&(), [out_share])?);
+                (agg_share, outbound)
+            }
+            (
+                DapVersion::Draft09,
+                Prio3Config::Draft09SumVecField64MultiproofHmacSha256Aes128 {
+                    bits,
+                    length,
+                    chunk_length,
+                    num_proofs,
+                },
+                VdafPrepState::Prio3Draft09Field64HmacSha256Aes128(state),
+                VdafPrepShare::Prio3Draft09Field64HmacSha256Aes128(share),
+            ) => {
+                let vdaf = prio3_draft09::new_prio3_sum_vec_field64_multiproof_hmac_sha256_aes128(
+                    *bits,
+                    *length,
+                    *chunk_length,
+                    *num_proofs,
+                )?;
+                let (out_share, outbound) = super::prep_finish_from_shares_draft09(
+                    &vdaf,
+                    agg_id,
+                    state,
+                    share,
+                    peer_share_data,
+                )?;
+                let agg_share = VdafAggregateShare::Field64Draft09(
+                    prio_draft09::vdaf::Aggregator::aggregate(&vdaf, &(), [out_share])?,
+                );
+                (agg_share, outbound)
+            }
+            _ => {
+                return Err(VdafError::Dap(fatal_error!(
+                    err = format!(
+                    "unexpected prep state or share or {self:?} is not supported in DAP {version}"
+                )
+                )))
+            }
+        };
 
-    type Prio3Prepared<T, const SEED_SIZE: usize> = (
-        Prio3PrepareState<<T as Type>::Field, SEED_SIZE>,
-        Prio3PrepareShare<<T as Type>::Field, SEED_SIZE>,
-    );
+        Ok((agg_share, outbound))
+    }
 
-    fn prep_init<T, P, const SEED_SIZE: usize>(
-        vdaf: Prio3<T, P, SEED_SIZE>,
+    pub(crate) fn prep_finish(
+        &self,
+        host_state: VdafPrepState,
+        peer_message_data: &[u8],
         task_id: TaskId,
-        verify_key: &[u8; SEED_SIZE],
-        agg_id: usize,
-        nonce: &[u8; 16],
-        public_share_data: &[u8],
-        input_share_data: &[u8],
-    ) -> Result<Prio3Prepared<T, SEED_SIZE>, VdafError>
-    where
-        T: Type,
-        P: Xof<SEED_SIZE>,
-    {
-        // Parse the public share.
-        let public_share = Prio3PublicShare::get_decoded_with_param(&vdaf, public_share_data)?;
-
-        // Parse the input share.
-        let input_share =
-            Prio3InputShare::get_decoded_with_param(&(&vdaf, agg_id), input_share_data)?;
+        version: DapVersion,
+    ) -> Result<VdafAggregateShare, VdafError> {
+        let agg_share = match (version, self, host_state) {
+            (DapVersion::Latest, Prio3Config::Count, VdafPrepState::Prio3Field64(state)) => {
+                let vdaf = Prio3::new_count(2).map_err(|e| {
+                    VdafError::Dap(fatal_error!(err = ?e, "initializing {self:?} failed"))
+                })?;
+                let out_share = prep_finish(&vdaf, task_id, state, peer_message_data)?;
+                VdafAggregateShare::Field64(vdaf.aggregate(&(), [out_share])?)
+            }
+            (
+                DapVersion::Latest,
+                Prio3Config::Sum { max_measurement },
+                VdafPrepState::Prio3Field64(state),
+            ) => {
+                let vdaf = Prio3::new_sum(2, *max_measurement).map_err(|e| {
+                    VdafError::Dap(fatal_error!(err = ?e, "initializing {self:?} failed"))
+                })?;
+                let out_share = prep_finish(&vdaf, task_id, state, peer_message_data)?;
+                VdafAggregateShare::Field64(vdaf.aggregate(&(), [out_share])?)
+            }
+            (
+                DapVersion::Latest,
+                Prio3Config::Histogram {
+                    length,
+                    chunk_length,
+                },
+                VdafPrepState::Prio3Field128(state),
+            ) => {
+                let vdaf = Prio3::new_histogram(2, *length, *chunk_length).map_err(|e| {
+                    VdafError::Dap(fatal_error!(err = ?e, "initializing {self:?} failed"))
+                })?;
+                let out_share = prep_finish(&vdaf, task_id, state, peer_message_data)?;
+                VdafAggregateShare::Field128(vdaf.aggregate(&(), [out_share])?)
+            }
+            (
+                DapVersion::Latest,
+                Prio3Config::SumVec {
+                    bits,
+                    length,
+                    chunk_length,
+                },
+                VdafPrepState::Prio3Field128(state),
+            ) => {
+                let vdaf = Prio3::new_sum_vec(2, *bits, *length, *chunk_length).map_err(|e| {
+                    VdafError::Dap(fatal_error!(err = ?e, "initializing {self:?} failed"))
+                })?;
+                let out_share = prep_finish(&vdaf, task_id, state, peer_message_data)?;
+                VdafAggregateShare::Field128(vdaf.aggregate(&(), [out_share])?)
+            }
+            (
+                DapVersion::Draft09,
+                Prio3Config::Draft09SumVecField64MultiproofHmacSha256Aes128 {
+                    bits,
+                    length,
+                    chunk_length,
+                    num_proofs,
+                },
+                VdafPrepState::Prio3Draft09Field64HmacSha256Aes128(state),
+            ) => {
+                let vdaf = prio3_draft09::new_prio3_sum_vec_field64_multiproof_hmac_sha256_aes128(
+                    *bits,
+                    *length,
+                    *chunk_length,
+                    *num_proofs,
+                )?;
+                let out_share = super::prep_finish_draft09(&vdaf, state, peer_message_data)?;
+                VdafAggregateShare::Field64Draft09(prio_draft09::vdaf::Aggregator::aggregate(
+                    &vdaf,
+                    &(),
+                    [out_share],
+                )?)
+            }
+            _ => {
+                return Err(VdafError::Dap(fatal_error!(
+                    err = format!(
+                        "unexpected prep state or {self:?} is not supported in DAP {version}"
+                    )
+                )))
+            }
+        };
 
-        let mut ctx = [0; CTX_STRING_PREFIX.len() + 32];
-        ctx[..CTX_STRING_PREFIX.len()].copy_from_slice(CTX_STRING_PREFIX);
-        ctx[CTX_STRING_PREFIX.len()..].copy_from_slice(&task_id.0);
-        // Run the prepare-init algorithm, returning the initial state.
-        Ok(vdaf.prepare_init(
-            verify_key,
-            &ctx,
-            agg_id,
-            &(),
-            nonce,
-            &public_share,
-            &input_share,
-        )?)
+        Ok(agg_share)
     }
-}
 
-/// Consume the prep shares and return our output share and the prep message.
-pub(crate) fn prio3_prep_finish_from_shares(
-    config: &Prio3Config,
-    agg_id: usize,
-    task_id: TaskId,
-    host_state: VdafPrepState,
-    host_share: VdafPrepShare,
-    peer_share_data: &[u8],
-) -> Result<(VdafAggregateShare, Vec<u8>), VdafError> {
-    let (agg_share, outbound) = match (&config, host_state, host_share) {
-        (
-            Prio3Config::Count,
-            VdafPrepState::Prio3Field64(state),
-            VdafPrepShare::Prio3Field64(share),
-        ) => {
-            let vdaf = Prio3::new_count(2).map_err(|e| {
-                VdafError::Dap(
-                    fatal_error!(err = ?e, "failed to create prio3 count num_aggregators(2)"),
-                )
-            })?;
-            let (out_share, outbound) =
-                prep_finish_from_shares(&vdaf, task_id, agg_id, state, share, peer_share_data)?;
-            let agg_share = VdafAggregateShare::Field64(vdaf.aggregate(&(), [out_share])?);
-            (agg_share, outbound)
-        }
-        (
-            Prio3Config::Histogram {
-                length,
-                chunk_length,
-            },
-            VdafPrepState::Prio3Field128(state),
-            VdafPrepShare::Prio3Field128(share),
-        ) => {
-            let vdaf = Prio3::new_histogram(2, *length, *chunk_length)
-                .map_err(|e| VdafError::Dap(fatal_error!(err = ?e, "failed to create prio3 histogram from num_aggregators(2), length({length}), chunk_length({chunk_length})")))?;
-            let (out_share, outbound) =
-                prep_finish_from_shares(&vdaf, task_id, agg_id, state, share, peer_share_data)?;
-            let agg_share = VdafAggregateShare::Field128(vdaf.aggregate(&(), [out_share])?);
-            (agg_share, outbound)
-        }
-        (
-            Prio3Config::Sum { .. },
-            VdafPrepState::Prio3Field128(_),
-            VdafPrepShare::Prio3Field128(_),
-        ) => Err(VdafError::Dap(fatal_error!(err = "Prio3Sum is not supported in VDAF-13")))?,
-        (
-            Prio3Config::SumVec {
-                bits,
-                length,
-                chunk_length,
-            },
-            VdafPrepState::Prio3Field128(state),
-            VdafPrepShare::Prio3Field128(share),
-        ) => {
-            let vdaf = Prio3::new_sum_vec(2, *bits, *length, *chunk_length)
-                .map_err(|e| VdafError::Dap(fatal_error!(err = ?e, "failed to create prio3 sum vec from num_aggregators(2), bits({bits}), length({length}), chunk_length({chunk_length})")))?;
-            let (out_share, outbound) =
-                prep_finish_from_shares(&vdaf, task_id, agg_id, state, share, peer_share_data)?;
-            let agg_share = VdafAggregateShare::Field128(vdaf.aggregate(&(), [out_share])?);
-            (agg_share, outbound)
-        }
-        (
-            Prio3Config::SumVecField64MultiproofHmacSha256Aes128 {
-            ..
-        },
-            VdafPrepState::Prio3Field64HmacSha256Aes128(_),
-            VdafPrepShare::Prio3Field64HmacSha256Aes128(_),
-        ) => {
-            return Err(VdafError::Dap(fatal_error!(err = format!("prio3_prep_finish_from_shares: SumVecField64MultiproofHmacSha256Aes128 is not defined for VDAF-13"))))
-        }
-        _ => {
-            return Err(VdafError::Dap(fatal_error!(
-                err = format!("prio3_prep_finish_from_shares: unexpected field type for step or message")
-            )))
-        }
-    };
+    pub(crate) fn unshard<M: IntoIterator<Item = Vec<u8>>>(
+        &self,
+        version: DapVersion,
+        num_measurements: usize,
+        agg_shares: M,
+    ) -> Result<DapAggregateResult, VdafError> {
+        match (version, self) {
+            (DapVersion::Latest, Prio3Config::Count) => {
+                let vdaf = Prio3::new_count(2).map_err(|e| {
+                    VdafError::Dap(fatal_error!(err = ?e, "initializing {self:?} failed"))
+                })?;
 
-    Ok((agg_share, outbound))
-}
+                let agg_res = unshard(&vdaf, num_measurements, agg_shares)?;
+                Ok(DapAggregateResult::U64(agg_res))
+            }
+            (DapVersion::Latest, Prio3Config::Sum { max_measurement }) => {
+                let vdaf = Prio3::new_sum(2, *max_measurement).map_err(|e| {
+                    VdafError::Dap(fatal_error!(err = ?e, "initializing {self:?} failed"))
+                })?;
 
-/// Consume the prep message and output our output share.
-pub(crate) fn prio3_prep_finish(
-    config: &Prio3Config,
-    host_state: VdafPrepState,
-    peer_message_data: &[u8],
-    task_id: TaskId,
-) -> Result<VdafAggregateShare, VdafError> {
-    let agg_share = match (&config, host_state) {
-        (Prio3Config::Count, VdafPrepState::Prio3Field64(state)) => {
-            let vdaf = Prio3::new_count(2).map_err(|e| {
-                VdafError::Dap(
-                    fatal_error!(err = ?e, "failed to create prio3 count from num_aggregators(2)"),
-                )
-            })?;
-            let out_share = prep_finish(&vdaf, task_id, state, peer_message_data)?;
-            VdafAggregateShare::Field64(vdaf.aggregate(&(), [out_share])?)
-        }
-        (
-            Prio3Config::Histogram {
-                length,
-                chunk_length,
-            },
-            VdafPrepState::Prio3Field128(state),
-        ) => {
-            let vdaf = Prio3::new_histogram(2, *length, *chunk_length)
-                .map_err(|e| VdafError::Dap(fatal_error!(err = ?e, "failed to create prio3 histogram from num_aggregators(2), length({length}), chunk_length({chunk_length})")))?;
-            let out_share = prep_finish(&vdaf, task_id, state, peer_message_data)?;
-            VdafAggregateShare::Field128(vdaf.aggregate(&(), [out_share])?)
-        }
-        (Prio3Config::Sum { .. }, VdafPrepState::Prio3Field128(_)) => {
-            Err(VdafError::Dap(fatal_error!(err = "sum unimplemented")))?
-        }
-        (
-            Prio3Config::SumVec {
-                bits,
-                length,
-                chunk_length,
-            },
-            VdafPrepState::Prio3Field128(state),
-        ) => {
-            let vdaf = Prio3::new_sum_vec(2, *bits, *length, *chunk_length)
-                .map_err(|e| VdafError::Dap(fatal_error!(err = ?e, "failed to create prio3 sum vec from num_aggregators(2), bits({bits}), length({length}), chunk_length({chunk_length})")))?;
-            let out_share = prep_finish(&vdaf, task_id, state, peer_message_data)?;
-            VdafAggregateShare::Field128(vdaf.aggregate(&(), [out_share])?)
-        }
-        (
-            Prio3Config::SumVecField64MultiproofHmacSha256Aes128 {
-            ..
-            },
-            VdafPrepState::Prio3Field64HmacSha256Aes128(_),
-        ) => {
+                let agg_res = unshard(&vdaf, num_measurements, agg_shares)?;
+                Ok(DapAggregateResult::U64(agg_res))
+            }
+            (
+                DapVersion::Latest,
+                Prio3Config::Histogram {
+                    length,
+                    chunk_length,
+                },
+            ) => {
+                let vdaf = Prio3::new_histogram(2, *length, *chunk_length).map_err(|e| {
+                    VdafError::Dap(fatal_error!(err = ?e, "initializing {self:?} failed"))
+                })?;
 
-            return Err(VdafError::Dap(fatal_error!(err = format!("prio3_prep_finish: SumVecField64MultiproofHmacSha256Aes128 is not defined for VDAF-13"))))
-        }
+                let agg_res = unshard(&vdaf, num_measurements, agg_shares)?;
+                Ok(DapAggregateResult::U128Vec(agg_res))
+            }
+            (
+                DapVersion::Latest,
+                Prio3Config::SumVec {
+                    bits,
+                    length,
+                    chunk_length,
+                },
+            ) => {
+                let vdaf = Prio3::new_sum_vec(2, *bits, *length, *chunk_length).map_err(|e| {
+                    VdafError::Dap(fatal_error!(err = ?e, "initializing {self:?} failed"))
+                })?;
 
-        _ => {
-            return Err(VdafError::Dap(fatal_error!(
-                err = format!("prio3_prep_finish: unexpected field type for step or message")
-            )))
-        }
-    };
-
-    Ok(agg_share)
-}
-
-/// Interpret `agg_shares` as a sequence of encoded aggregate shares and unshard them.
-pub(crate) fn prio3_unshard<M: IntoIterator<Item = Vec<u8>>>(
-    config: &Prio3Config,
-    num_measurements: usize,
-    agg_shares: M,
-) -> Result<DapAggregateResult, VdafError> {
-    match config {
-        Prio3Config::Count => {
-            let vdaf = Prio3::new_count(2).map_err(|e| {
-                VdafError::Dap(
-                    fatal_error!(err = ?e, "failed to create prio3 count from num_aggregators(2)"),
-                )
-            })?;
-            let agg_res = unshard(&vdaf, num_measurements, agg_shares)?;
-            Ok(DapAggregateResult::U64(agg_res))
-        }
-        Prio3Config::Histogram {
-            length,
-            chunk_length,
-        } => {
-            let vdaf = Prio3::new_histogram(2, *length, *chunk_length)
-                .map_err(|e| VdafError::Dap(fatal_error!(err = ?e, "failed to create prio3 histogram from num_aggregators(2), length({length}), chunk_length({chunk_length})")))?;
-            let agg_res = unshard(&vdaf, num_measurements, agg_shares)?;
-            Ok(DapAggregateResult::U128Vec(agg_res))
-        }
-        Prio3Config::Sum { .. } => Err(VdafError::Dap(fatal_error!(err = "sum unimplemented"))),
-        Prio3Config::SumVec {
-            bits,
-            length,
-            chunk_length,
-        } => {
-            let vdaf = Prio3::new_sum_vec(2, *bits, *length, *chunk_length)
-                .map_err(|e| VdafError::Dap(fatal_error!(err = ?e, "failed to create prio3 sum vec from num_aggregators(2), bits({bits}), length({length}), chunk_length({chunk_length})")))?;
-            let agg_res = unshard(&vdaf, num_measurements, agg_shares)?;
-            Ok(DapAggregateResult::U128Vec(agg_res))
-        }
-        Prio3Config::SumVecField64MultiproofHmacSha256Aes128 {
-        ..
-        } => {
-            Err(VdafError::Dap(fatal_error!(err = format!("prio3_prep_finish: SumVecField64MultiproofHmacSha256Aes128 is not defined for VDAF-13"))))
+                let agg_res = unshard(&vdaf, num_measurements, agg_shares)?;
+                Ok(DapAggregateResult::U128Vec(agg_res))
+            }
+            (
+                DapVersion::Draft09,
+                Prio3Config::Draft09SumVecField64MultiproofHmacSha256Aes128 {
+                    bits,
+                    length,
+                    chunk_length,
+                    num_proofs,
+                },
+            ) => {
+                let vdaf = prio3_draft09::new_prio3_sum_vec_field64_multiproof_hmac_sha256_aes128(
+                    *bits,
+                    *length,
+                    *chunk_length,
+                    *num_proofs,
+                )?;
+                let agg_res = super::unshard_draft09(&vdaf, num_measurements, agg_shares)?;
+                Ok(DapAggregateResult::U64Vec(agg_res))
+            }
+            _ => Err(VdafError::Dap(fatal_error!(
+                err = format!("{version} does not support {self:?}")
+            ))),
         }
     }
 }
@@ -413,17 +570,17 @@ mod test {
 
     use crate::{
         hpke::HpkeKemId,
-        test_versions,
         testing::AggregationJobTest,
         vdaf::{Prio3Config, VdafConfig},
         DapAggregateResult, DapAggregationParam, DapMeasurement, DapVersion,
     };
 
-    fn roundtrip_count(version: DapVersion) {
+    #[test]
+    fn roundtrip_count() {
         let mut t = AggregationJobTest::new(
             &VdafConfig::Prio3(Prio3Config::Count),
             HpkeKemId::X25519HkdfSha256,
-            version,
+            DapVersion::Latest,
         );
         let got = t.roundtrip(
             DapAggregationParam::Empty,
@@ -438,9 +595,30 @@ mod test {
         assert_eq!(got, DapAggregateResult::U64(3));
     }
 
-    test_versions! { roundtrip_count }
+    #[test]
+    fn roundtrip_sum() {
+        let mut t = AggregationJobTest::new(
+            &VdafConfig::Prio3(Prio3Config::Sum {
+                max_measurement: 1337,
+            }),
+            HpkeKemId::X25519HkdfSha256,
+            DapVersion::Latest,
+        );
+        let got = t.roundtrip(
+            DapAggregationParam::Empty,
+            vec![
+                DapMeasurement::U64(0),
+                DapMeasurement::U64(1),
+                DapMeasurement::U64(1337),
+                DapMeasurement::U64(4),
+                DapMeasurement::U64(0),
+            ],
+        );
+        assert_eq!(got, DapAggregateResult::U64(1342));
+    }
 
-    fn roundtrip_sum_vec(version: DapVersion) {
+    #[test]
+    fn roundtrip_sum_vec() {
         let mut t = AggregationJobTest::new(
             &VdafConfig::Prio3(Prio3Config::SumVec {
                 bits: 23,
@@ -448,7 +626,7 @@ mod test {
                 chunk_length: 1,
             }),
             HpkeKemId::X25519HkdfSha256,
-            version,
+            DapVersion::Latest,
         );
         let got = t.roundtrip(
             DapAggregationParam::Empty,
@@ -461,16 +639,15 @@ mod test {
         assert_eq!(got, DapAggregateResult::U128Vec(vec![1338, 1338]));
     }
 
-    test_versions! { roundtrip_sum_vec }
-
-    fn roundtrip_histogram(version: DapVersion) {
+    #[test]
+    fn roundtrip_histogram() {
         let mut t = AggregationJobTest::new(
             &VdafConfig::Prio3(Prio3Config::Histogram {
                 length: 3,
                 chunk_length: 1,
             }),
             HpkeKemId::X25519HkdfSha256,
-            version,
+            DapVersion::Latest,
         );
         let got = t.roundtrip(
             DapAggregationParam::Empty,
@@ -484,6 +661,4 @@ mod test {
         );
         assert_eq!(got, DapAggregateResult::U128Vec(vec![1, 1, 3]));
     }
-
-    test_versions! { roundtrip_histogram }
 }
diff --git a/crates/daphne/src/vdaf/prio3_draft09.rs b/crates/daphne/src/vdaf/prio3_draft09.rs
index bd13f30bc..93800e783 100644
--- a/crates/daphne/src/vdaf/prio3_draft09.rs
+++ b/crates/daphne/src/vdaf/prio3_draft09.rs
@@ -4,16 +4,8 @@
 //! Parameters for the [Prio3 VDAF](https://datatracker.ietf.org/doc/draft-irtf-cfrg-vdaf/09/).
 
 use crate::{
-    fatal_error,
-    messages::taskprov::VDAF_TYPE_PRIO3_SUM_VEC_FIELD64_MULTIPROOF_HMAC_SHA256_AES128,
-    vdaf::{VdafError, VdafVerifyKey},
-    DapAggregateResult, DapMeasurement, Prio3Config, VdafAggregateShare, VdafPrepShare,
-    VdafPrepState,
-};
-
-use super::{
-    prep_finish_draft09, prep_finish_from_shares_draft09, shard_then_encode_draft09,
-    unshard_draft09,
+    fatal_error, messages::taskprov::VDAF_TYPE_PRIO3_SUM_VEC_FIELD64_MULTIPROOF_HMAC_SHA256_AES128,
+    vdaf::VdafError,
 };
 
 use prio_draft09::{
@@ -31,12 +23,10 @@ use prio_draft09::{
     },
 };
 
-const ERR_FIELD_TYPE: &str = "unexpected field type for step or message";
-
 type Prio3SumVecField64MultiproofHmacSha256Aes128 =
     Prio3<SumVec<Field64, ParallelSum<Field64, Mul<Field64>>>, XofHmacSha256Aes128, 32>;
 
-fn new_prio3_sum_vec_field64_multiproof_hmac_sha256_aes128(
+pub(crate) fn new_prio3_sum_vec_field64_multiproof_hmac_sha256_aes128(
     bits: usize,
     length: usize,
     chunk_length: usize,
@@ -56,458 +46,31 @@ fn new_prio3_sum_vec_field64_multiproof_hmac_sha256_aes128(
     .map_err(|e| VdafError::Dap(fatal_error!(err = ?e, "failed to create prio3")))
 }
 
-/// Split the given measurement into a sequence of encoded input shares.
-pub(crate) fn prio3_draft09_shard(
-    config: &Prio3Config,
-    measurement: DapMeasurement,
-    nonce: &[u8; 16],
-) -> Result<(Vec<u8>, [Vec<u8>; 2]), VdafError> {
-    match (config, measurement) {
-        (Prio3Config::Count, DapMeasurement::U64(measurement)) if measurement < 2 => {
-            let vdaf = Prio3::new_count(2).map_err(|e| {
-                VdafError::Dap(
-                    fatal_error!(err = ?e, "failed to create prio3 count from num_aggregators(2)"),
-                )
-            })?;
-            shard_then_encode_draft09(&vdaf, &(measurement != 0), nonce)
-        }
-        (
-            Prio3Config::Histogram {
-                length,
-                chunk_length,
-            },
-            DapMeasurement::U64(measurement),
-        ) => {
-            let vdaf = Prio3::new_histogram(2, *length, *chunk_length)
-                .map_err(|e| VdafError::Dap(fatal_error!(err = ?e, "failed to create prio3 Histogram from num_aggregators(2), length({length}), chunk_length({chunk_length})")))?;
-            let m: usize = measurement.try_into().unwrap();
-            shard_then_encode_draft09(&vdaf, &m, nonce)
-        }
-        (Prio3Config::Sum { bits }, DapMeasurement::U64(measurement)) => {
-            let vdaf =
-                Prio3::new_sum(2, *bits).map_err(|e| VdafError::Dap(fatal_error!(err = ?e, "failed to create prio3 sum from num_aggregators(2), bits({bits})")))?;
-            shard_then_encode_draft09(&vdaf, &u128::from(measurement), nonce)
-        }
-        (
-            Prio3Config::SumVec {
-                bits,
-                length,
-                chunk_length,
-            },
-            DapMeasurement::U128Vec(measurement),
-        ) => {
-            let vdaf = Prio3::new_sum_vec(2, *bits, *length, *chunk_length)
-                .map_err(|e| VdafError::Dap(fatal_error!(err = ?e, "failed to create prio3 sum vec from num_aggregators(2), bits({bits}), length({length}), chunk_length({chunk_length})")))?;
-            shard_then_encode_draft09(&vdaf, &measurement, nonce)
-        }
-        (
-            Prio3Config::SumVecField64MultiproofHmacSha256Aes128 {
-                bits,
-                length,
-                chunk_length,
-                num_proofs,
-            },
-            DapMeasurement::U64Vec(measurement),
-        ) => {
-            let vdaf = new_prio3_sum_vec_field64_multiproof_hmac_sha256_aes128(
-                *bits,
-                *length,
-                *chunk_length,
-                *num_proofs,
-            )?;
-            shard_then_encode_draft09(&vdaf, &measurement, nonce)
-        }
-        _ => Err(VdafError::Dap(fatal_error!(
-            err = format!("prio3_shard: unexpected VDAF config {config:?}")
-        ))),
-    }
-}
+type Prio3Draft09Prepared<T, const SEED_SIZE: usize> = (
+    Prio3PrepareState<<T as Type>::Field, SEED_SIZE>,
+    Prio3PrepareShare<<T as Type>::Field, SEED_SIZE>,
+);
 
-/// Consume an input share and return the corresponding VDAF step and message.
-pub(crate) fn prio3_draft09_prep_init(
-    config: &Prio3Config,
-    verify_key: &VdafVerifyKey,
+pub(crate) fn prep_init_draft09<T, P, const SEED_SIZE: usize>(
+    vdaf: Prio3<T, P, SEED_SIZE>,
+    verify_key: &[u8; SEED_SIZE],
     agg_id: usize,
     nonce: &[u8; 16],
     public_share_data: &[u8],
     input_share_data: &[u8],
-) -> Result<(VdafPrepState, VdafPrepShare), VdafError> {
-    return match (&config, verify_key) {
-        (Prio3Config::Count, VdafVerifyKey::L16(verify_key)) => {
-            let vdaf = Prio3::new_count(2).map_err(|e| {
-                VdafError::Dap(
-                    fatal_error!(err = ?e, "failed to create prio3 from num_aggregators(2)"),
-                )
-            })?;
-            let (state, share) = prep_init_draft09(
-                vdaf,
-                verify_key,
-                agg_id,
-                nonce,
-                public_share_data,
-                input_share_data,
-            )?;
-            Ok((
-                VdafPrepState::Prio3Draft09Field64(state),
-                VdafPrepShare::Prio3Draft09Field64(share),
-            ))
-        }
-        (
-            Prio3Config::Histogram {
-                length,
-                chunk_length,
-            },
-            VdafVerifyKey::L16(verify_key),
-        ) => {
-            let vdaf = Prio3::new_histogram(2, *length, *chunk_length)
-                .map_err(|e| VdafError::Dap(fatal_error!(err = ?e, "failed to create prio3 histogram from num_aggregators(2), length({length}), chunk_length({chunk_length})")))?;
-            let (state, share) = prep_init_draft09(
-                vdaf,
-                verify_key,
-                agg_id,
-                nonce,
-                public_share_data,
-                input_share_data,
-            )?;
-            Ok((
-                VdafPrepState::Prio3Draft09Field128(state),
-                VdafPrepShare::Prio3Draft09Field128(share),
-            ))
-        }
-        (Prio3Config::Sum { bits }, VdafVerifyKey::L16(verify_key)) => {
-            let vdaf =
-                Prio3::new_sum(2, *bits).map_err(|e| VdafError::Dap(fatal_error!(err = ?e, "failed to create prio3 sum from num_aggregators(2), bits({bits})")))?;
-            let (state, share) = prep_init_draft09(
-                vdaf,
-                verify_key,
-                agg_id,
-                nonce,
-                public_share_data,
-                input_share_data,
-            )?;
-            Ok((
-                VdafPrepState::Prio3Draft09Field128(state),
-                VdafPrepShare::Prio3Draft09Field128(share),
-            ))
-        }
-        (
-            Prio3Config::SumVec {
-                bits,
-                length,
-                chunk_length,
-            },
-            VdafVerifyKey::L16(verify_key),
-        ) => {
-            let vdaf = Prio3::new_sum_vec(2, *bits, *length, *chunk_length)
-                .map_err(|e| VdafError::Dap(fatal_error!(err = ?e, "failed to create prio3 sum vec from num_aggregators(2), bits({bits}), length({length}), chunk_length({chunk_length})")))?;
-            let (state, share) = prep_init_draft09(
-                vdaf,
-                verify_key,
-                agg_id,
-                nonce,
-                public_share_data,
-                input_share_data,
-            )?;
-            Ok((
-                VdafPrepState::Prio3Draft09Field128(state),
-                VdafPrepShare::Prio3Draft09Field128(share),
-            ))
-        }
-        (
-            Prio3Config::SumVecField64MultiproofHmacSha256Aes128 {
-                bits,
-                length,
-                chunk_length,
-                num_proofs,
-            },
-            VdafVerifyKey::L32(verify_key),
-        ) => {
-            let vdaf = new_prio3_sum_vec_field64_multiproof_hmac_sha256_aes128(
-                *bits,
-                *length,
-                *chunk_length,
-                *num_proofs,
-            )?;
-            let (state, share) = prep_init_draft09(
-                vdaf,
-                verify_key,
-                agg_id,
-                nonce,
-                public_share_data,
-                input_share_data,
-            )?;
-            Ok((
-                VdafPrepState::Prio3Draft09Field64HmacSha256Aes128(state),
-                VdafPrepShare::Prio3Draft09Field64HmacSha256Aes128(share),
-            ))
-        }
-        _ => {
-            return Err(VdafError::Dap(fatal_error!(
-                err = "unhandled config and verify key combination",
-            )))
-        }
-    };
-
-    type Prio3Draft09Prepared<T, const SEED_SIZE: usize> = (
-        Prio3PrepareState<<T as Type>::Field, SEED_SIZE>,
-        Prio3PrepareShare<<T as Type>::Field, SEED_SIZE>,
-    );
-
-    fn prep_init_draft09<T, P, const SEED_SIZE: usize>(
-        vdaf: Prio3<T, P, SEED_SIZE>,
-        verify_key: &[u8; SEED_SIZE],
-        agg_id: usize,
-        nonce: &[u8; 16],
-        public_share_data: &[u8],
-        input_share_data: &[u8],
-    ) -> Result<Prio3Draft09Prepared<T, SEED_SIZE>, VdafError>
-    where
-        T: Type,
-        P: Xof<SEED_SIZE>,
-    {
-        // Parse the public share.
-        let public_share = Prio3PublicShare::get_decoded_with_param(&vdaf, public_share_data)?;
-
-        // Parse the input share.
-        let input_share =
-            Prio3InputShare::get_decoded_with_param(&(&vdaf, agg_id), input_share_data)?;
-
-        // Run the prepare-init algorithm, returning the initial state.
-        Ok(vdaf.prepare_init(verify_key, agg_id, &(), nonce, &public_share, &input_share)?)
-    }
-}
-
-/// Consume the prep shares and return our output share and the prep message.
-pub(crate) fn prio3_draft09_prep_finish_from_shares(
-    config: &Prio3Config,
-    agg_id: usize,
-    host_state: VdafPrepState,
-    host_share: VdafPrepShare,
-    peer_share_data: &[u8],
-) -> Result<(VdafAggregateShare, Vec<u8>), VdafError> {
-    let (agg_share, outbound) = match (&config, host_state, host_share) {
-        (
-            Prio3Config::Count,
-            VdafPrepState::Prio3Draft09Field64(state),
-            VdafPrepShare::Prio3Draft09Field64(share),
-        ) => {
-            let vdaf = Prio3::new_count(2).map_err(|e| {
-                VdafError::Dap(
-                    fatal_error!(err = ?e, "failed to create prio3 count num_aggregators(2)"),
-                )
-            })?;
-            let (out_share, outbound) =
-                prep_finish_from_shares_draft09(&vdaf, agg_id, state, share, peer_share_data)?;
-            let agg_share = VdafAggregateShare::Field64Draft09(vdaf.aggregate(&(), [out_share])?);
-            (agg_share, outbound)
-        }
-        (
-            Prio3Config::Histogram {
-                length,
-                chunk_length,
-            },
-            VdafPrepState::Prio3Draft09Field128(state),
-            VdafPrepShare::Prio3Draft09Field128(share),
-        ) => {
-            let vdaf = Prio3::new_histogram(2, *length, *chunk_length)
-                .map_err(|e| VdafError::Dap(fatal_error!(err = ?e, "failed to create prio3 histogram from num_aggregators(2), length({length}), chunk_length({chunk_length})")))?;
-            let (out_share, outbound) =
-                prep_finish_from_shares_draft09(&vdaf, agg_id, state, share, peer_share_data)?;
-            let agg_share = VdafAggregateShare::Field128Draft09(vdaf.aggregate(&(), [out_share])?);
-            (agg_share, outbound)
-        }
-        (
-            Prio3Config::Sum { bits },
-            VdafPrepState::Prio3Draft09Field128(state),
-            VdafPrepShare::Prio3Draft09Field128(share),
-        ) => {
-            let vdaf =
-                Prio3::new_sum(2, *bits).map_err(|e| VdafError::Dap(fatal_error!(err = ?e, "failed to create prio3 sum from num_aggregators(2), bits({bits})")))?;
-            let (out_share, outbound) =
-                prep_finish_from_shares_draft09(&vdaf, agg_id, state, share, peer_share_data)?;
-            let agg_share = VdafAggregateShare::Field128Draft09(vdaf.aggregate(&(), [out_share])?);
-            (agg_share, outbound)
-        }
-        (
-            Prio3Config::SumVec {
-                bits,
-                length,
-                chunk_length,
-            },
-            VdafPrepState::Prio3Draft09Field128(state),
-            VdafPrepShare::Prio3Draft09Field128(share),
-        ) => {
-            let vdaf = Prio3::new_sum_vec(2, *bits, *length, *chunk_length)
-                .map_err(|e| VdafError::Dap(fatal_error!(err = ?e, "failed to create prio3 sum vec from num_aggregators(2), bits({bits}), length({length}), chunk_length({chunk_length})")))?;
-            let (out_share, outbound) =
-                prep_finish_from_shares_draft09(&vdaf, agg_id, state, share, peer_share_data)?;
-            let agg_share = VdafAggregateShare::Field128Draft09(vdaf.aggregate(&(), [out_share])?);
-            (agg_share, outbound)
-        }
-        (
-            Prio3Config::SumVecField64MultiproofHmacSha256Aes128 {
-                bits,
-                length,
-                chunk_length,
-                num_proofs,
-            },
-            VdafPrepState::Prio3Draft09Field64HmacSha256Aes128(state),
-            VdafPrepShare::Prio3Draft09Field64HmacSha256Aes128(share),
-        ) => {
-            let vdaf = new_prio3_sum_vec_field64_multiproof_hmac_sha256_aes128(
-                *bits,
-                *length,
-                *chunk_length,
-                *num_proofs,
-            )?;
-            let (out_share, outbound) =
-                prep_finish_from_shares_draft09(&vdaf, agg_id, state, share, peer_share_data)?;
-            let agg_share = VdafAggregateShare::Field64Draft09(vdaf.aggregate(&(), [out_share])?);
-            (agg_share, outbound)
-        }
-        _ => {
-            return Err(VdafError::Dap(fatal_error!(
-                err = format!("prio3_prep_finish_from_shares: {ERR_FIELD_TYPE}")
-            )))
-        }
-    };
-
-    Ok((agg_share, outbound))
-}
-
-/// Consume the prep message and output our output share.
-pub(crate) fn prio3_draft09_prep_finish(
-    config: &Prio3Config,
-    host_state: VdafPrepState,
-    peer_message_data: &[u8],
-) -> Result<VdafAggregateShare, VdafError> {
-    let agg_share = match (&config, host_state) {
-        (Prio3Config::Count, VdafPrepState::Prio3Draft09Field64(state)) => {
-            let vdaf = Prio3::new_count(2).map_err(|e| {
-                VdafError::Dap(
-                    fatal_error!(err = ?e, "failed to create prio3 count from num_aggregators(2)"),
-                )
-            })?;
-            let out_share = prep_finish_draft09(&vdaf, state, peer_message_data)?;
-            VdafAggregateShare::Field64Draft09(vdaf.aggregate(&(), [out_share])?)
-        }
-        (
-            Prio3Config::Histogram {
-                length,
-                chunk_length,
-            },
-            VdafPrepState::Prio3Draft09Field128(state),
-        ) => {
-            let vdaf = Prio3::new_histogram(2, *length, *chunk_length)
-                .map_err(|e| VdafError::Dap(fatal_error!(err = ?e, "failed to create prio3 histogram from num_aggregators(2), length({length}), chunk_length({chunk_length})")))?;
-            let out_share = prep_finish_draft09(&vdaf, state, peer_message_data)?;
-            VdafAggregateShare::Field128Draft09(vdaf.aggregate(&(), [out_share])?)
-        }
-        (Prio3Config::Sum { bits }, VdafPrepState::Prio3Draft09Field128(state)) => {
-            let vdaf =
-                Prio3::new_sum(2, *bits).map_err(|e| VdafError::Dap(fatal_error!(err = ?e, "failed to create prio3 sum from num_aggregators(2), bits({bits})")))?;
-            let out_share = prep_finish_draft09(&vdaf, state, peer_message_data)?;
-            VdafAggregateShare::Field128Draft09(vdaf.aggregate(&(), [out_share])?)
-        }
-        (
-            Prio3Config::SumVec {
-                bits,
-                length,
-                chunk_length,
-            },
-            VdafPrepState::Prio3Draft09Field128(state),
-        ) => {
-            let vdaf = Prio3::new_sum_vec(2, *bits, *length, *chunk_length)
-                .map_err(|e| VdafError::Dap(fatal_error!(err = ?e, "failed to create prio3 sum vec from num_aggregators(2), bits({bits}), length({length}), chunk_length({chunk_length})")))?;
-            let out_share = prep_finish_draft09(&vdaf, state, peer_message_data)?;
-            VdafAggregateShare::Field128Draft09(vdaf.aggregate(&(), [out_share])?)
-        }
-        (
-            Prio3Config::SumVecField64MultiproofHmacSha256Aes128 {
-                bits,
-                length,
-                chunk_length,
-                num_proofs,
-            },
-            VdafPrepState::Prio3Draft09Field64HmacSha256Aes128(state),
-        ) => {
-            let vdaf = new_prio3_sum_vec_field64_multiproof_hmac_sha256_aes128(
-                *bits,
-                *length,
-                *chunk_length,
-                *num_proofs,
-            )?;
-            let out_share = prep_finish_draft09(&vdaf, state, peer_message_data)?;
-            VdafAggregateShare::Field64Draft09(vdaf.aggregate(&(), [out_share])?)
-        }
-
-        _ => {
-            return Err(VdafError::Dap(fatal_error!(
-                err = format!("prio3_prep_finish: {ERR_FIELD_TYPE}")
-            )))
-        }
-    };
-
-    Ok(agg_share)
-}
-
-/// Interpret `agg_shares` as a sequence of encoded aggregate shares and unshard them.
-pub(crate) fn prio3_draft09_unshard<M: IntoIterator<Item = Vec<u8>>>(
-    config: &Prio3Config,
-    num_measurements: usize,
-    agg_shares: M,
-) -> Result<DapAggregateResult, VdafError> {
-    match config {
-        Prio3Config::Count => {
-            let vdaf = Prio3::new_count(2).map_err(|e| {
-                VdafError::Dap(
-                    fatal_error!(err = ?e, "failed to create prio3 count from num_aggregators(2)"),
-                )
-            })?;
-            let agg_res = unshard_draft09(&vdaf, num_measurements, agg_shares)?;
-            Ok(DapAggregateResult::U64(agg_res))
-        }
-        Prio3Config::Histogram {
-            length,
-            chunk_length,
-        } => {
-            let vdaf = Prio3::new_histogram(2, *length, *chunk_length)
-                .map_err(|e| VdafError::Dap(fatal_error!(err = ?e, "failed to create prio3 histogram from num_aggregators(2), length({length}), chunk_length({chunk_length})")))?;
-            let agg_res = unshard_draft09(&vdaf, num_measurements, agg_shares)?;
-            Ok(DapAggregateResult::U128Vec(agg_res))
-        }
-        Prio3Config::Sum { bits } => {
-            let vdaf =
-                Prio3::new_sum(2, *bits).map_err(|e| VdafError::Dap(fatal_error!(err = ?e, "failed to create prio3 sum from num_aggregators(2), bits({bits})")))?;
-            let agg_res = unshard_draft09(&vdaf, num_measurements, agg_shares)?;
-            Ok(DapAggregateResult::U128(agg_res))
-        }
-        Prio3Config::SumVec {
-            bits,
-            length,
-            chunk_length,
-        } => {
-            let vdaf = Prio3::new_sum_vec(2, *bits, *length, *chunk_length)
-                .map_err(|e| VdafError::Dap(fatal_error!(err = ?e, "failed to create prio3 sum vec from num_aggregators(2), bits({bits}), length({length}), chunk_length({chunk_length})")))?;
-            let agg_res = unshard_draft09(&vdaf, num_measurements, agg_shares)?;
-            Ok(DapAggregateResult::U128Vec(agg_res))
-        }
-        Prio3Config::SumVecField64MultiproofHmacSha256Aes128 {
-            bits,
-            length,
-            chunk_length,
-            num_proofs,
-        } => {
-            let vdaf = new_prio3_sum_vec_field64_multiproof_hmac_sha256_aes128(
-                *bits,
-                *length,
-                *chunk_length,
-                *num_proofs,
-            )?;
-            let agg_res = unshard_draft09(&vdaf, num_measurements, agg_shares)?;
-            Ok(DapAggregateResult::U64Vec(agg_res))
-        }
-    }
+) -> Result<Prio3Draft09Prepared<T, SEED_SIZE>, VdafError>
+where
+    T: Type,
+    P: Xof<SEED_SIZE>,
+{
+    // Parse the public share.
+    let public_share = Prio3PublicShare::get_decoded_with_param(&vdaf, public_share_data)?;
+
+    // Parse the input share.
+    let input_share = Prio3InputShare::get_decoded_with_param(&(&vdaf, agg_id), input_share_data)?;
+
+    // Run the prepare-init algorithm, returning the initial state.
+    Ok(vdaf.prepare_init(verify_key, agg_id, &(), nonce, &public_share, &input_share)?)
 }
 
 #[cfg(test)]
@@ -517,7 +80,6 @@ mod test {
 
     use crate::{
         hpke::HpkeKemId,
-        test_versions,
         testing::AggregationJobTest,
         vdaf::{
             prio3_draft09::new_prio3_sum_vec_field64_multiproof_hmac_sha256_aes128, Prio3Config,
@@ -526,105 +88,19 @@ mod test {
         DapAggregateResult, DapAggregationParam, DapMeasurement, DapVersion,
     };
 
-    fn roundtrip_count(version: DapVersion) {
-        let mut t = AggregationJobTest::new(
-            &VdafConfig::Prio3Draft09(Prio3Config::Count),
-            HpkeKemId::X25519HkdfSha256,
-            version,
-        );
-        let got = t.roundtrip(
-            DapAggregationParam::Empty,
-            vec![
-                DapMeasurement::U64(0),
-                DapMeasurement::U64(1),
-                DapMeasurement::U64(1),
-                DapMeasurement::U64(1),
-                DapMeasurement::U64(0),
-            ],
-        );
-        assert_eq!(got, DapAggregateResult::U64(3));
-    }
-
-    test_versions! { roundtrip_count }
-
-    fn roundtrip_sum(version: DapVersion) {
-        let mut t = AggregationJobTest::new(
-            &VdafConfig::Prio3Draft09(Prio3Config::Sum { bits: 23 }),
-            HpkeKemId::X25519HkdfSha256,
-            version,
-        );
-        let got = t.roundtrip(
-            DapAggregationParam::Empty,
-            vec![
-                DapMeasurement::U64(0),
-                DapMeasurement::U64(1),
-                DapMeasurement::U64(1337),
-                DapMeasurement::U64(4),
-                DapMeasurement::U64(0),
-            ],
-        );
-        assert_eq!(got, DapAggregateResult::U128(1342));
-    }
-
-    test_versions! { roundtrip_sum }
-
-    fn roundtrip_sum_vec(version: DapVersion) {
-        let mut t = AggregationJobTest::new(
-            &VdafConfig::Prio3Draft09(Prio3Config::SumVec {
-                bits: 23,
-                length: 2,
-                chunk_length: 1,
-            }),
-            HpkeKemId::X25519HkdfSha256,
-            version,
-        );
-        let got = t.roundtrip(
-            DapAggregationParam::Empty,
-            vec![
-                DapMeasurement::U128Vec(vec![1337, 0]),
-                DapMeasurement::U128Vec(vec![0, 1337]),
-                DapMeasurement::U128Vec(vec![1, 1]),
-            ],
-        );
-        assert_eq!(got, DapAggregateResult::U128Vec(vec![1338, 1338]));
-    }
-
-    test_versions! { roundtrip_sum_vec }
-
-    fn roundtrip_histogram(version: DapVersion) {
-        let mut t = AggregationJobTest::new(
-            &VdafConfig::Prio3Draft09(Prio3Config::Histogram {
-                length: 3,
-                chunk_length: 1,
-            }),
-            HpkeKemId::X25519HkdfSha256,
-            version,
-        );
-        let got = t.roundtrip(
-            DapAggregationParam::Empty,
-            vec![
-                DapMeasurement::U64(0),
-                DapMeasurement::U64(1),
-                DapMeasurement::U64(2),
-                DapMeasurement::U64(2),
-                DapMeasurement::U64(2),
-            ],
-        );
-        assert_eq!(got, DapAggregateResult::U128Vec(vec![1, 1, 3]));
-    }
-
-    test_versions! { roundtrip_histogram }
-
-    fn roundtrip_sum_vec_field64_multiproof_hmac_sha256_aes128(version: DapVersion) {
+    #[test]
+    fn roundtrip_sum_vec_field64_multiproof_hmac_sha256_aes128_draft09() {
         let mut t = AggregationJobTest::new(
-            &VdafConfig::Prio3Draft09(Prio3Config::SumVecField64MultiproofHmacSha256Aes128 {
-                bits: 23,
-                length: 2,
-                chunk_length: 1,
-                num_proofs: 4,
-            }),
+            &VdafConfig::Prio3(
+                Prio3Config::Draft09SumVecField64MultiproofHmacSha256Aes128 {
+                    bits: 23,
+                    length: 2,
+                    chunk_length: 1,
+                    num_proofs: 4,
+                },
+            ),
             HpkeKemId::X25519HkdfSha256,
-            version,
+            DapVersion::Draft09,
         );
         let got = t.roundtrip(
             DapAggregationParam::Empty,
@@ -637,8 +113,6 @@ mod test {
         assert_eq!(got, DapAggregateResult::U64Vec(vec![1338, 1338]));
     }
 
-    test_versions! { roundtrip_sum_vec_field64_multiproof_hmac_sha256_aes128 }
-
     #[test]
     fn test_vec_sum_vec_field64_multiproof_hmac_sha256_aes128() {
         for test_vec_json_str in [