diff --git a/dask_ml/model_selection/_incremental.py b/dask_ml/model_selection/_incremental.py
index 4697cbec6..4056f35ec 100644
--- a/dask_ml/model_selection/_incremental.py
+++ b/dask_ml/model_selection/_incremental.py
@@ -203,12 +203,13 @@ async def _fit(
     y_train = sorted(futures_of(y_train), key=lambda f: f.key)
     assert len(X_train) == len(y_train)
 
-    train_eg = await client.gather(client.map(len, y_train))
-    msg = "[CV%s] For training there are between %d and %d examples in each chunk"
-    logger.info(msg, prefix, min(train_eg), max(train_eg))
+    train_eg = await client.gather(client.map(len, X_train))
 
-    # Order by which we process training data futures
-    order = []
+    min_samples = min(train_eg) if len(train_eg) else len(X_train)
+    max_samples = max(train_eg) if len(train_eg) else len(X_train)
+
+    msg = "[CV%s] For training there are between %d and %d examples in each chunk"
+    logger.info(msg, prefix, min_samples, max_samples)
 
     def get_futures(partial_fit_calls):
         """Policy to get training data futures
@@ -218,6 +219,9 @@ def get_futures(partial_fit_calls):
         This function handles that policy internally, and also controls random
         access to training data.
         """
+        if dask.is_dask_collection(X_train):
+            return X_train, y_train
+
         # Shuffle blocks going forward to get uniform-but-random access
         while partial_fit_calls >= len(order):
             L = list(range(len(X_train)))
@@ -226,6 +230,9 @@ def get_futures(partial_fit_calls):
         j = order[partial_fit_calls]
         return X_train[j], y_train[j]
 
+    # Order by which we process training data futures
+    order = []
+
     # Submit initial partial_fit and score computations on first batch of data
     X_future, y_future = get_futures(0)
     X_future_2, y_future_2 = get_futures(1)
@@ -566,7 +573,8 @@ def _get_train_test_split(self, X, y, **kwargs):
         X, y : dask.array.Array
         """
         if self.test_size is None:
-            test_size = min(0.2, 1 / X.npartitions)
+            npartitions = getattr(X, 'npartitions', 1)
+            test_size = min(0.2, 1 / npartitions)
         else:
             test_size = self.test_size
         X_train, X_test, y_train, y_test = train_test_split(
diff --git a/tests/model_selection/test_hyperband.py b/tests/model_selection/test_hyperband.py
index 9bcf131aa..6e31fddc4 100644
--- a/tests/model_selection/test_hyperband.py
+++ b/tests/model_selection/test_hyperband.py
@@ -14,6 +14,7 @@
     loop,
 )
 from sklearn.linear_model import SGDClassifier
+from sklearn.datasets import make_classification as sk_make_classification
 
 from dask_ml._compat import DISTRIBUTED_2_5_0
 from dask_ml.datasets import make_classification
@@ -478,3 +479,19 @@ async def test_dataframe_inputs(c, s, a, b):
     params = {"value": scipy.stats.uniform(0, 1)}
     alg = HyperbandSearchCV(model, params, max_iter=9, random_state=42)
     await alg.fit(X, y)
+
+
+@gen_cluster(client=True)
+def test_pandas(c, s, a, b):
+
+    X, y = sk_make_classification()
+    X, y = pd.DataFrame(X), pd.Series(y)
+
+    est = SGDClassifier(tol=1e-3)
+    param_dist = {'alpha': np.logspace(-4, 0, num=1000),
+                  'loss': ['hinge', 'log', 'modified_huber', 'squared_hinge'],
+                  'average': [True, False]}
+
+    search = HyperbandSearchCV(est, param_dist)
+    yield search.fit(X, y, classes=y.unique())
+    assert search.best_params_