diff --git a/tests/test_functions.py b/tests/test_functions.py
index b6aa7984..0841a1a6 100644
--- a/tests/test_functions.py
+++ b/tests/test_functions.py
@@ -1677,21 +1677,25 @@ def test_constrain_ages_topo(self):
         ts = utility_functions.two_tree_ts()
         post_mn = np.array([0.0, 0.0, 0.0, 2.0, 1.0, 3.0])
         eps = 1e-6
-        nodes_to_date = np.array([3, 4, 5])
-        constrained_ages = constrain_ages_topo(ts, post_mn, eps, nodes_to_date)
+        constrained_ages = constrain_ages_topo(ts, post_mn, eps)
         assert np.array_equal(
             np.array([0.0, 0.0, 0.0, 2.0, 2.000001, 3.0]), constrained_ages
         )
 
-    def test_constrain_ages_topo_no_nodes_to_date(self):
+    def test_constrain_ages_topo_node_order_bug(self):
+        """
+        Previous version of constrain_ages_topo had a bug where it was
+        assumed that node IDs were in time order, although this is not
+        guaranteed by tskit.
+        """
         ts = utility_functions.two_tree_ts()
-        post_mn = np.array([0.0, 0.0, 0.0, 2.0, 1.0, 3.0])
+        ts = ts.subset([0, 1, 5, 3, 4, 2])  # alter the node order
+        post_mn = np.array([3.0, 0.0, 0.0, 0.0, 0.0, 0.0])
         eps = 1e-6
-        nodes_to_date = None
-        constrained_ages = constrain_ages_topo(ts, post_mn, eps, nodes_to_date)
-        assert np.array_equal(
-            np.array([0.0, 0.0, 0.0, 2.0, 2.000001, 3.0]), constrained_ages
-        )
+        constrained_ages = constrain_ages_topo(ts, post_mn, eps)
+        tables = ts.dump_tables()
+        tables.nodes.time = constrained_ages
+        tables.sort()
 
     def test_constrain_ages_topo_unary_nodes_unordered(self):
         ts = utility_functions.single_tree_ts_with_unary()
diff --git a/tsdate/core.py b/tsdate/core.py
index c007b009..fe80ca49 100644
--- a/tsdate/core.py
+++ b/tsdate/core.py
@@ -1096,37 +1096,33 @@ def posterior_mean_var(ts, posterior, *, fixed_node_set=None):
     return ts, mn_post, vr_post
 
 
-def constrain_ages_topo(ts, post_mn, eps, nodes_to_date=None, progress=False):
+def constrain_ages_topo(ts, node_times, eps, progress=False):
     """
-    If predicted node times violate topology, restrict node ages so that they
-    must be older than all their children.
+    If node_times violate topology, return increased node_times so that each node is
+    guaranteed to be older than any of its their children.
     """
-    new_mn_post = np.copy(post_mn)
-    if nodes_to_date is None:
-        nodes_to_date = np.arange(ts.num_nodes, dtype=np.uint64)
-        nodes_to_date = nodes_to_date[~np.isin(nodes_to_date, ts.samples())]
-
-    tables = ts.tables
-    parents = tables.edges.parent
-    nd_children = tables.edges.child[np.argsort(parents)]
-    parents = sorted(parents)
-    parents_unique = np.unique(parents, return_index=True)
-    parent_indices = parents_unique[1][np.isin(parents_unique[0], nodes_to_date)]
-    for index, nd in tqdm(
-        enumerate(sorted(nodes_to_date)),
+    edges_parent = ts.edges_parent
+    edges_child = ts.edges_child
+
+    new_node_times = np.copy(node_times)
+    # Traverse through the ARG, ensuring children come before parents.
+    # This can be done by iterating over groups of edges with the same parent
+    new_parent_edge_idx = np.where(np.diff(edges_parent) != 0)[0] + 1
+    for edges_start, edges_end in tqdm(
+        zip(
+            itertools.chain([0], new_parent_edge_idx),
+            itertools.chain(new_parent_edge_idx, [len(edges_parent)]),
+        ),
         desc="Constrain Ages",
-        total=len(nodes_to_date),
+        total=len(new_parent_edge_idx) + 1,
         disable=not progress,
     ):
-        if index + 1 != len(nodes_to_date):
-            children_index = np.arange(parent_indices[index], parent_indices[index + 1])
-        else:
-            children_index = np.arange(parent_indices[index], ts.num_edges)
-        children = nd_children[children_index]
-        time = np.max(new_mn_post[children])
-        if new_mn_post[nd] <= time:
-            new_mn_post[nd] = time + eps
-    return new_mn_post
+        parent = edges_parent[edges_start]
+        child_ids = edges_child[edges_start:edges_end]  # May contain dups
+        oldest_child_time = np.max(new_node_times[child_ids])
+        if oldest_child_time >= new_node_times[parent]:
+            new_node_times[parent] = oldest_child_time + eps
+    return new_node_times
 
 
 def date(
@@ -1254,7 +1250,7 @@ def date(
             method=method,
             **kwargs,
         )
-    constrained = constrain_ages_topo(tree_sequence, dates, eps, nds, progress)
+    constrained = constrain_ages_topo(tree_sequence, dates, eps, progress)
     tables = tree_sequence.dump_tables()
     tables.time_units = time_units
     tables.nodes.time = constrained