diff --git a/c/tests/test_tables.c b/c/tests/test_tables.c
index 0b9ff088e5..04ed2b1ceb 100644
--- a/c/tests/test_tables.c
+++ b/c/tests/test_tables.c
@@ -10775,6 +10775,85 @@ test_check_integrity_bad_mutation_parent_topology(void)
     tsk_table_collection_free(&tables);
 }
 
+static void
+test_table_collection_compute_mutation_parents_tolerates_invalid_input(void)
+{
+    int ret;
+    tsk_id_t ret_id;
+    tsk_table_collection_t tables;
+    tsk_id_t site;
+
+    ret = tsk_table_collection_init(&tables, 0);
+    CU_ASSERT_EQUAL_FATAL(ret, 0);
+    tables.sequence_length = 1.0;
+
+    ret_id = tsk_node_table_add_row(&tables.nodes, 0, 1.0, TSK_NULL, TSK_NULL, NULL, 0);
+    CU_ASSERT_FATAL(ret_id >= 0);
+    ret_id = tsk_node_table_add_row(
+        &tables.nodes, TSK_NODE_IS_SAMPLE, 0.0, TSK_NULL, TSK_NULL, NULL, 0);
+    CU_ASSERT_FATAL(ret_id >= 0);
+    ret_id = tsk_edge_table_add_row(&tables.edges, 0.0, 1.0, 0, 1, NULL, 0);
+    CU_ASSERT_EQUAL_FATAL(ret_id, 0);
+    site = tsk_site_table_add_row(&tables.sites, 0.0, "A", 1, NULL, 0);
+    CU_ASSERT_FATAL(site >= 0);
+    ret_id = tsk_mutation_table_add_row(
+        &tables.mutations, site, 1, TSK_NULL, TSK_UNKNOWN_TIME, "C", 1, NULL, 0);
+    CU_ASSERT_EQUAL_FATAL(ret_id, 0);
+
+    ret = tsk_table_collection_build_index(&tables, 0);
+    CU_ASSERT_EQUAL_FATAL(ret, 0);
+    tables.mutations.parent[0] = 42;
+
+    ret = tsk_table_collection_compute_mutation_parents(&tables, 0);
+    CU_ASSERT_EQUAL_FATAL(ret, 0);
+    CU_ASSERT_FATAL(tables.mutations.parent[0] == TSK_NULL);
+
+    tsk_table_collection_free(&tables);
+}
+
+static void
+test_table_collection_compute_mutation_parents_restores_on_error(void)
+{
+    int ret;
+    tsk_id_t ret_id;
+    tsk_table_collection_t tables;
+    tsk_id_t site;
+
+    ret = tsk_table_collection_init(&tables, 0);
+    CU_ASSERT_EQUAL_FATAL(ret, 0);
+    tables.sequence_length = 1.0;
+
+    ret_id = tsk_node_table_add_row(&tables.nodes, 0, 1.0, TSK_NULL, TSK_NULL, NULL, 0);
+    CU_ASSERT_FATAL(ret_id >= 0);
+    ret_id = tsk_node_table_add_row(
+        &tables.nodes, TSK_NODE_IS_SAMPLE, 0.0, TSK_NULL, TSK_NULL, NULL, 0);
+    CU_ASSERT_FATAL(ret_id >= 0);
+    ret_id = tsk_edge_table_add_row(&tables.edges, 0.0, 1.0, 0, 1, NULL, 0);
+    CU_ASSERT_EQUAL_FATAL(ret_id, 0);
+    site = tsk_site_table_add_row(&tables.sites, 0.5, "A", 1, NULL, 0);
+    CU_ASSERT_FATAL(site >= 0);
+
+    ret_id = tsk_mutation_table_add_row(
+        &tables.mutations, site, 1, TSK_NULL, TSK_UNKNOWN_TIME, "C", 1, NULL, 0);
+    CU_ASSERT_FATAL(ret_id >= 0);
+    ret_id = tsk_mutation_table_add_row(
+        &tables.mutations, site, 0, TSK_NULL, TSK_UNKNOWN_TIME, "G", 1, NULL, 0);
+    CU_ASSERT_FATAL(ret_id >= 0);
+
+    ret = tsk_table_collection_build_index(&tables, 0);
+    CU_ASSERT_EQUAL_FATAL(ret, 0);
+
+    tables.mutations.parent[0] = 111;
+    tables.mutations.parent[1] = 222;
+
+    ret = tsk_table_collection_compute_mutation_parents(&tables, 0);
+    CU_ASSERT_EQUAL_FATAL(ret, TSK_ERR_MUTATION_PARENT_AFTER_CHILD);
+    CU_ASSERT_EQUAL(tables.mutations.parent[0], 111);
+    CU_ASSERT_EQUAL(tables.mutations.parent[1], 222);
+
+    tsk_table_collection_free(&tables);
+}
+
 static void
 test_table_collection_subset_with_options(tsk_flags_t options)
 {
@@ -11934,6 +12013,10 @@ main(int argc, char **argv)
             test_table_collection_check_integrity_bad_indexes },
         { "test_check_integrity_bad_mutation_parent_topology",
             test_check_integrity_bad_mutation_parent_topology },
+        { "test_table_collection_compute_mutation_parents_tolerates_invalid_input",
+            test_table_collection_compute_mutation_parents_tolerates_invalid_input },
+        { "test_table_collection_compute_mutation_parents_restores_on_error",
+            test_table_collection_compute_mutation_parents_restores_on_error },
         { "test_table_collection_subset", test_table_collection_subset },
         { "test_table_collection_subset_unsorted",
             test_table_collection_subset_unsorted },
diff --git a/c/tskit/tables.c b/c/tskit/tables.c
index 7106300f3d..4a256df27f 100644
--- a/c/tskit/tables.c
+++ b/c/tskit/tables.c
@@ -12436,8 +12436,27 @@ tsk_table_collection_compute_mutation_parents(
     tsk_table_collection_t *self, tsk_flags_t options)
 {
     int ret = 0;
+    tsk_mutation_table_t *mutations = &self->mutations;
+    tsk_id_t *parent_backup = NULL;
+    bool restore_parents = false;
 
     if (!(options & TSK_NO_CHECK_INTEGRITY)) {
+        if (mutations->num_rows > 0) {
+            /* We need to wipe the parent column before computing, as otherwise invalid
+             * parents can cause integrity checks to fail. We take a copy to restore on
+             * error */
+            parent_backup = tsk_malloc(mutations->num_rows * sizeof(*parent_backup));
+            if (parent_backup == NULL) {
+                ret = tsk_trace_error(TSK_ERR_NO_MEMORY);
+                goto out;
+            }
+            tsk_memcpy(parent_backup, mutations->parent,
+                mutations->num_rows * sizeof(*parent_backup));
+            /* Set the parent pointers to TSK_NULL */
+            tsk_memset(mutations->parent, 0xff,
+                mutations->num_rows * sizeof(*mutations->parent));
+            restore_parents = true;
+        }
         /* Safe to cast here as we're not counting trees */
         ret = (int) tsk_table_collection_check_integrity(self, TSK_CHECK_TREES);
         if (ret < 0) {
@@ -12452,6 +12471,11 @@ tsk_table_collection_compute_mutation_parents(
     }
 
 out:
+    if (ret != 0 && restore_parents) {
+        tsk_memcpy(mutations->parent, parent_backup,
+            mutations->num_rows * sizeof(*parent_backup));
+    }
+    tsk_safe_free(parent_backup);
     return ret;
 }
 
diff --git a/python/tests/test_tables.py b/python/tests/test_tables.py
index 6971780b47..dc9dfb4c97 100644
--- a/python/tests/test_tables.py
+++ b/python/tests/test_tables.py
@@ -3540,6 +3540,34 @@ def test_table_references(self):
         assert str(populations) == before_populations
         assert str(provenances) == before_provenances
 
+    def test_compute_mutation_parents_ignores_existing_values(self):
+        tables = tskit.TableCollection(sequence_length=1.0)
+        parent = tables.nodes.add_row(time=1.0)
+        child = tables.nodes.add_row(time=0, flags=tskit.NODE_IS_SAMPLE)
+        tables.edges.add_row(left=0.0, right=1.0, parent=parent, child=child)
+        site = tables.sites.add_row(position=0.0, ancestral_state="A")
+        tables.mutations.add_row(site=site, node=child, derived_state="C")
+        tables.build_index()
+        tables.mutations.parent[:] = 42
+        tables.compute_mutation_parents()
+        assert tables.mutations.parent[0] == tskit.NULL
+
+    def test_compute_mutation_parents_restores_on_index_error(self):
+        tables = tskit.TableCollection(sequence_length=1.0)
+        parent = tables.nodes.add_row(time=1.0)
+        child = tables.nodes.add_row(time=0, flags=tskit.NODE_IS_SAMPLE)
+        tables.edges.add_row(left=0.0, right=1.0, parent=parent, child=child)
+        site = tables.sites.add_row(position=0.0, ancestral_state="A")
+        tables.mutations.add_row(site=site, node=child, derived_state="C")
+
+        mutation_columns = tables.mutations.asdict()
+        mutation_columns["parent"] = np.array([123], dtype=np.int32)
+        tables.mutations.set_columns(**mutation_columns)
+
+        with pytest.raises(tskit.LibraryError, match="TSK_ERR_TABLES_NOT_INDEXED"):
+            tables.compute_mutation_parents()
+        assert tables.mutations.parent[0] == 123
+
     def test_str(self):
         ts = msprime.simulate(10, random_seed=1)
         tables = ts.tables