diff --git a/khmer/khmer_args.py b/khmer/khmer_args.py
index 8f233e4efa..c71d9c52f8 100755
--- a/khmer/khmer_args.py
+++ b/khmer/khmer_args.py
@@ -50,6 +50,8 @@
 import screed
 import khmer
 from khmer import extract_countgraph_info
+from khmer import Nodegraph, Countgraph, SmallCountgraph
+from khmer import Nodetable, Counttable, CyclicCounttable, SmallCounttable
 from khmer import __version__
 from .utils import print_error
 from .khmer_logger import log_info, log_warn, configure_logging
@@ -560,14 +562,22 @@ def create_countgraph(args, ksize=None, multiplier=1.0, fp_rate=0.1):
         print_error("\n** ERROR: khmer only supports k-mer sizes <= 32.\n")
         sys.exit(1)
 
+    dotable = hasattr(args, 'hash_function') and args.hash_function == 'murmur'
+    docyclic = hasattr(args, 'hash_function') and args.hash_function == 'cyclic'
     if args.small_count:
         tablesize = calculate_graphsize(args, 'smallcountgraph',
                                         multiplier=multiplier)
-        return khmer.SmallCountgraph(ksize, tablesize, args.n_tables)
+        constructor = SmallCounttable if dotable else SmallCountgraph
+        return constructor(ksize, tablesize, args.n_tables)
     else:
         tablesize = calculate_graphsize(args, 'countgraph',
                                         multiplier=multiplier)
-        cg = khmer.Countgraph(ksize, tablesize, args.n_tables)
+        constructor = Countgraph
+        if dotable:
+            constructor = Counttable
+        elif docyclic:
+            constructor = CyclicCounttable
+        cg = constructor(ksize, tablesize, args.n_tables)
         if hasattr(args, 'bigcount'):
             cg.set_use_bigcount(args.bigcount)
         return cg
diff --git a/scripts/abundance-dist-single.py b/scripts/abundance-dist-single.py
index 7fcf580276..34ba715eb0 100755
--- a/scripts/abundance-dist-single.py
+++ b/scripts/abundance-dist-single.py
@@ -84,6 +84,15 @@ def get_parser():
                         'output histogram file. The columns are: (1) k-mer '
                         'abundance, (2) k-mer count, (3) cumulative count, '
                         '(4) fraction of total distinct k-mers.')
+    parser.add_argument('-H', '--hash-function', choices=['2bit', 'murmur',
+                        'cyclic'], default='2bit', help='Indicate the hash '
+                        'function to be used; "2bit" is faster, is reversible,'
+                        ' and supports subsequent graph operations, but is '
+                        'limited to k <= 32; "murmur" supports arbitrarily '
+                        'large values of k and is compatible with k-mer '
+                        'banding, but is slower and does not support graph '
+                        'operations; "cyclic" is fast and supports banding, '
+                        'but does not support graph operations')
     parser.add_argument('-z', '--no-zero', dest='output_zero', default=True,
                         action='store_false',
                         help='Do not output zero-count bins')
@@ -98,6 +107,15 @@ def get_parser():
                         "filename.")
     parser.add_argument('-f', '--force', default=False, action='store_true',
                         help='Override sanity checks')
+    parser.add_argument('--banding', type=int, nargs=2, default=False,
+                        metavar=('N', 'B'), help='process k-mers in "banding" '
+                        'mode; specify two integers: a number of bands "N", '
+                        'and a band index "B" such that B is between 1 and N '
+                        'inclusive; as a result, only 1/N k-mers will be '
+                        'processed, resulting in a roughly N-fold reduction '
+                        'in memory consumption; for example, "--banding 50 9" '
+                        'will split the k-mer space into 50 bands and only '
+                        'process k-mers in band 9')
     parser.add_argument('-q', '--quiet', dest='quiet', default=False,
                         action='store_true')
     return parser
@@ -106,6 +124,9 @@ def get_parser():
 def main():  # pylint: disable=too-many-locals,too-many-branches
     args = sanitize_help(get_parser()).parse_args()
     graph_type = 'smallcountgraph' if args.small_count else 'countgraph'
+    if args.banding and args.hash_function == '2bit':
+        message = 'can only process in "banding" mode with "murmur" hash'
+        raise ValueError(message)
 
     configure_logging(args.quiet)
     report_on_config(args, graph_type)
@@ -145,8 +166,15 @@ def main():  # pylint: disable=too-many-locals,too-many-branches
     log_info('consuming input, round 1 -- {input}',
              input=args.input_sequence_filename)
     for _ in range(args.threads):
-        thread = \
-            threading.Thread(
+        if args.banding:
+            numbands = args.banding[0]
+            bandindex = args.banding[1] - 1  # CLI is 1-based, API is 0-based
+            thread = threading.Thread(
+                target=countgraph.consume_seqfile_banding,
+                args=(rparser, numbands, bandindex, )
+            )
+        else:
+            thread = threading.Thread(
                 target=countgraph.consume_seqfile,
                 args=(rparser, )
             )