diff --git a/python/tests/test_divmat.py b/python/tests/test_divmat.py
index 91b84e84b2..bf5118a5d4 100644
--- a/python/tests/test_divmat.py
+++ b/python/tests/test_divmat.py
@@ -163,7 +163,7 @@ def span_normalise_windows(D, windows):
 
 def branch_divergence_matrix(ts, windows=None, samples=None, span_normalise=True):
     windows_specified = windows is not None
-    windows = [0, ts.sequence_length] if windows is None else windows
+    windows = ts.parse_windows(windows)
     num_windows = len(windows) - 1
     samples = ts.samples() if samples is None else samples
 
@@ -296,7 +296,7 @@ def group_alleles(genotypes, num_alleles):
 
 def site_divergence_matrix(ts, windows=None, samples=None, span_normalise=True):
     windows_specified = windows is not None
-    windows = [0, ts.sequence_length] if windows is None else windows
+    windows = ts.parse_windows(windows)
     num_windows = len(windows) - 1
     samples = ts.samples() if samples is None else samples
 
@@ -954,6 +954,8 @@ def check(self, ts, num_threads, *, windows, samples=None, mode=None):
             ([5, 7, 9, 20],),
             ([5.1, 5.2, 5.3, 5.5, 6],),
             ([5.1, 5.2, 6.5],),
+            ("trees",),
+            ("sites",),
         ],
     )
     @pytest.mark.parametrize("mode", DIVMAT_MODES)
@@ -968,6 +970,8 @@ def test_all_trees(self, num_threads, windows, mode):
         [
             ([0, 26],),
             (None,),
+            ("trees",),
+            ("sites",),
         ],
     )
     @pytest.mark.parametrize("mode", DIVMAT_MODES)
@@ -984,6 +988,8 @@ def test_all_trees_samples(self, samples, windows, mode):
             ([50, 75, 95, 100],),
             ([0, 50, 75, 95],),
             (list(range(100)),),
+            ("trees",),
+            ("sites",),
         ],
     )
     @pytest.mark.parametrize("mode", DIVMAT_MODES)
diff --git a/python/tests/test_lowlevel.py b/python/tests/test_lowlevel.py
index cf0b9c78c1..31ad272a05 100644
--- a/python/tests/test_lowlevel.py
+++ b/python/tests/test_lowlevel.py
@@ -1537,6 +1537,8 @@ def test_divergence_matrix(self):
         assert D.shape == (1, n, n)
         D = ts.divergence_matrix(windows, samples=[0, 1])
         assert D.shape == (1, 2, 2)
+        D = ts.divergence_matrix(windows, samples=[0, 1], span_normalise=True)
+        assert D.shape == (1, 2, 2)
         with pytest.raises(TypeError, match="str"):
             ts.divergence_matrix(windows, span_normalise="xdf")
         with pytest.raises(TypeError):
diff --git a/python/tskit/trees.py b/python/tskit/trees.py
index 0d27f1678c..2cc47b2959 100644
--- a/python/tskit/trees.py
+++ b/python/tskit/trees.py
@@ -7865,12 +7865,11 @@ def divergence_matrix(
         span_normalise=True,
     ):
         windows_specified = windows is not None
-        windows = [0, self.sequence_length] if windows is None else windows
-
+        windows = self.parse_windows(windows)
         mode = "site" if mode is None else mode
 
-        # NOTE: maybe we want to use a different default for num_threads here, just
-        # following the approach in GNN
+        # FIXME this logic should be merged into __run_windowed_stat if
+        # we generalise the num_threads argument to all stats.
         if num_threads <= 0:
             D = self._ll_tree_sequence.divergence_matrix(
                 windows,