diff --git a/src/seismicrna/cluster/compare.py b/src/seismicrna/cluster/compare.py
index 2d9a93cd..0e5641f5 100644
--- a/src/seismicrna/cluster/compare.py
+++ b/src/seismicrna/cluster/compare.py
@@ -124,7 +124,7 @@ def _compare_groups(func: Callable, mus1: np.ndarray, mus2: np.ndarray):
     _, n2 = mus2.shape
     return np.array([[func(mus1[:, cluster1], mus2[:, cluster2])
                       for cluster2 in range(n2)]
-                     for cluster1 in range(n1)])
+                     for cluster1 in range(n1)]).reshape((n1, n2))
 
 
 def calc_rmsd_groups(mus1: np.ndarray, mus2: np.ndarray):
@@ -157,14 +157,15 @@ def assign_clusterings(mus1: np.ndarray, mus2: np.ndarray):
     # the assignment problem in O(n³) time, and this naive approach runs
     # in O(n!) time, the latter is simpler and still sufficiently fast
     # when n is no more than about 6, which is almost always true.
-    best_assignment = list()
+    ns = np.arange(n)
+    best_assignment = ns
     min_cost = None
-    rows = list(range(n))
-    for columns in permutations(rows):
-        cost = np.sum(costs[rows, columns])
+    for cols in permutations(ns):
+        assignment = np.array(cols, dtype=int)
+        cost = np.sum(costs[ns, assignment])
         if min_cost is None or cost < min_cost:
-            min_cost = float(cost)
-            best_assignment = list(zip(rows, columns))
+            min_cost = cost
+            best_assignment = assignment
     return best_assignment
 
 
@@ -172,14 +173,16 @@ def calc_rms_nrmsd(run1: EmClustering, run2: EmClustering):
     """ Compute the root-mean-square NRMSD between the clusters. """
     costs = np.square(calc_nrmsd_groups(run1.p_mut, run2.p_mut))
     assignment = assign_clusterings(run1.p_mut, run2.p_mut)
-    return float(np.sqrt(np.mean([costs[i, j] for i, j in assignment])))
+    return float(np.sqrt(np.mean([costs[row, col]
+                                  for row, col in enumerate(assignment)])))
 
 
 def calc_mean_pearson(run1: EmClustering, run2: EmClustering):
     """ Compute the mean Pearson correlation between the clusters. """
     correlations = calc_pearson_groups(run1.p_mut, run2.p_mut)
     assignment = assign_clusterings(run1.p_mut, run2.p_mut)
-    return float(np.mean([correlations[i, j] for i, j in assignment]))
+    return float(np.mean([correlations[row, col]
+                          for row, col in enumerate(assignment)]))
 
 ########################################################################
 #                                                                      #
diff --git a/src/seismicrna/cluster/tests/compare_test.py b/src/seismicrna/cluster/tests/compare_test.py
new file mode 100644
index 00000000..999cf909
--- /dev/null
+++ b/src/seismicrna/cluster/tests/compare_test.py
@@ -0,0 +1,58 @@
+import unittest as ut
+import warnings
+from itertools import permutations
+
+import numpy as np
+
+from seismicrna.cluster.compare import assign_clusterings
+from seismicrna.core.array import calc_inverse
+
+rng = np.random.default_rng()
+
+
+class TestAssignClusterings(ut.TestCase):
+
+    def test_0_clusters(self):
+        for n in range(5):
+            x = np.empty((n, 0))
+            y = np.empty((n, 0))
+            self.assertTrue(np.array_equal(assign_clusterings(x, y),
+                                           np.empty(0, dtype=int)))
+
+    def test_0_positions(self):
+        for n in range(5):
+            x = np.empty((0, n))
+            y = np.empty((0, n))
+            with warnings.catch_warnings():
+                warnings.simplefilter("ignore", RuntimeWarning)
+                with np.errstate(invalid="ignore"):
+                    self.assertTrue(np.array_equal(assign_clusterings(x, y),
+                                                   np.arange(n)))
+
+    def test_1_cluster(self):
+        for n in range(1, 10):
+            x = rng.random((n, 1))
+            y = rng.random((n, 1))
+            self.assertTrue(np.array_equal(assign_clusterings(x, y),
+                                           np.array([0])))
+
+    def test_more_clusters(self):
+        for ncls in range(2, 5):
+            for npos in range(2, 8):
+                with self.subTest(ncls=ncls, npos=npos):
+                    x = rng.random((npos, ncls))
+                    for permutation in permutations(range(ncls)):
+                        cols = np.array(permutation)
+                        y = x[:, cols]
+                        self.assertTrue(np.array_equal(
+                            assign_clusterings(x, y),
+                            calc_inverse(cols)
+                        ))
+                        self.assertTrue(np.array_equal(
+                            assign_clusterings(y, x),
+                            cols
+                        ))
+
+
+if __name__ == "__main__":
+    ut.main()