diff --git a/CHANGES.rst b/CHANGES.rst
index 514c7700..4ef73761 100644
--- a/CHANGES.rst
+++ b/CHANGES.rst
@@ -8,13 +8,19 @@ development version
 * Added a ``--max-average-error-rate``/``--max-aer`` option to add a filter
   that checks if the number of expected errors divided by  read length is above a
   certain threshold. The expected errors are calculated the same as in
-  ``--max-expected-errors`` and dividing by read length helps for reads that
+  ``--max-expected-errors``, and dividing by read length helps for reads that
   have varying lengths.
 * :issue:`696`: Added a histogram of the lengths of removed poly-A tails to
   the report.
 * :issue:`696`: For paired-end data, ``--poly-a`` was changed to trim poly-T
-  "heads" on R2.
+  "heads" on R2 (this is still experimental as it is unclear whether that is
+  the desired behavior. Please give feedback!)
 * A poly-A tail is only removed if it is at least three nucleotides long.
+* :issue:`734`: Fixed misassignments during demultiplexing that would sometimes
+  happen when there are collisions between adapter sequences
+  (when the warning "sequence ... cannot be assigned uniquely" was printed).
+  Previously, sequences could incorrectly be assigned to an adapter that is not
+  actually the best match.
 
 v4.4 (2023-04-28)
 -----------------
diff --git a/src/cutadapt/adapters.py b/src/cutadapt/adapters.py
index 82a57c61..55b4b824 100644
--- a/src/cutadapt/adapters.py
+++ b/src/cutadapt/adapters.py
@@ -1309,8 +1309,7 @@ def _make_index(self) -> Tuple[List[int], "AdapterIndex"]:
                         if other_matches == matches and not has_warned:
                             self._warn_similar(adapter, other_adapter, k, s, matches)
                             has_warned = True
-                    else:
-                        index[s] = (adapter, errors, matches)
+                    index[s] = (adapter, errors, matches)
                     lengths.add(len(s))
             else:
                 n = len(sequence)
@@ -1326,8 +1325,7 @@ def _make_index(self) -> Tuple[List[int], "AdapterIndex"]:
                                     adapter, other_adapter, k, s, matches
                                 )
                                 has_warned = True
-                        else:
-                            index[s] = (adapter, errors, matches)
+                        index[s] = (adapter, errors, matches)
                 lengths.add(n)
         elapsed = time.time() - start_time
         logger.info(
diff --git a/tests/test_adapters.py b/tests/test_adapters.py
index 90b3076a..e9252e83 100644
--- a/tests/test_adapters.py
+++ b/tests/test_adapters.py
@@ -559,6 +559,18 @@ def test_indexed_prefix_adapters_with_n_wildcard():
         assert result.score == 6
 
 
+@pytest.mark.parametrize("sequence", ["ANGCATCATAAAAAAAAAA", "AAGCATCATAAAAAAAAAA"])
+def test_indexed_prefix_adapters_with_n_collision(sequence):
+    a1 = PrefixAdapter("AAGCGCCAT", max_errors=2, indels=False)
+    a2 = PrefixAdapter("AGGCATCAT", max_errors=2, indels=False)
+    ipa = IndexedPrefixAdapters([a1, a2])
+
+    result = ipa.match_to(sequence)
+
+    assert isinstance(result, RemoveBeforeMatch)
+    assert result.adapter is a2
+
+
 def test_inosine_wildcard():
     adapter = BackAdapter("CTGIAIT", max_errors=0, min_overlap=3)
     match = adapter.match_to("GGCTGAATTGGG")