diff --git a/src/backend/optimizer/plan/planner.c b/src/backend/optimizer/plan/planner.c
index a1873ce26d433..502ccbcea235a 100644
--- a/src/backend/optimizer/plan/planner.c
+++ b/src/backend/optimizer/plan/planner.c
@@ -436,12 +436,10 @@ standard_planner(Query *parse, const char *query_string, int cursorOptions,
 		Gather	   *gather = makeNode(Gather);
 
 		/*
-		 * If there are any initPlans attached to the formerly-top plan node,
-		 * move them up to the Gather node; same as we do for Material node in
-		 * materialize_finished_plan.
+		 * Top plan must not have any initPlans, else it shouldn't have been
+		 * marked parallel-safe.
 		 */
-		gather->plan.initPlan = top_plan->initPlan;
-		top_plan->initPlan = NIL;
+		Assert(top_plan->initPlan == NIL);
 
 		gather->plan.targetlist = top_plan->targetlist;
 		gather->plan.qual = NIL;
diff --git a/src/backend/optimizer/plan/setrefs.c b/src/backend/optimizer/plan/setrefs.c
index b56666398eaef..1812db7f2fd56 100644
--- a/src/backend/optimizer/plan/setrefs.c
+++ b/src/backend/optimizer/plan/setrefs.c
@@ -1542,7 +1542,19 @@ trivial_subqueryscan(SubqueryScan *plan)
 static Plan *
 clean_up_removed_plan_level(Plan *parent, Plan *child)
 {
-	/* We have to be sure we don't lose any initplans */
+	/*
+	 * We have to be sure we don't lose any initplans, so move any that were
+	 * attached to the parent plan to the child.  If we do move any, the child
+	 * is no longer parallel-safe.
+	 */
+	if (parent->initPlan)
+		child->parallel_safe = false;
+
+	/*
+	 * Attach plans this way so that parent's initplans are processed before
+	 * any pre-existing initplans of the child.  Probably doesn't matter, but
+	 * let's preserve the ordering just in case.
+	 */
 	child->initPlan = list_concat(parent->initPlan,
 								  child->initPlan);
 
diff --git a/src/backend/optimizer/plan/subselect.c b/src/backend/optimizer/plan/subselect.c
index 052263aea6da7..5f12b2ef9b017 100644
--- a/src/backend/optimizer/plan/subselect.c
+++ b/src/backend/optimizer/plan/subselect.c
@@ -2126,7 +2126,7 @@ SS_identify_outer_params(PlannerInfo *root)
  * This is separate from SS_attach_initplans because we might conditionally
  * create more initPlans during create_plan(), depending on which Path we
  * select.  However, Paths that would generate such initPlans are expected
- * to have included their cost already.
+ * to have included their cost and parallel-safety effects already.
  */
 void
 SS_charge_for_initplans(PlannerInfo *root, RelOptInfo *final_rel)
@@ -2182,8 +2182,10 @@ SS_charge_for_initplans(PlannerInfo *root, RelOptInfo *final_rel)
  * (In principle the initPlans could go in any node at or above where they're
  * referenced; but there seems no reason to put them any lower than the
  * topmost node, so we don't bother to track exactly where they came from.)
- * We do not touch the plan node's cost; the initplans should have been
- * accounted for in path costing.
+ *
+ * We do not touch the plan node's cost or parallel_safe flag.  The initplans
+ * must have been accounted for in SS_charge_for_initplans, or by any later
+ * code that adds initplans via SS_make_initplan_from_plan.
  */
 void
 SS_attach_initplans(PlannerInfo *root, Plan *plan)
diff --git a/src/backend/optimizer/util/pathnode.c b/src/backend/optimizer/util/pathnode.c
index 65a191ebfda97..5f5596841c86a 100644
--- a/src/backend/optimizer/util/pathnode.c
+++ b/src/backend/optimizer/util/pathnode.c
@@ -3348,7 +3348,7 @@ create_minmaxagg_path(PlannerInfo *root,
 	/* For now, assume we are above any joins, so no parameterization */
 	pathnode->path.param_info = NULL;
 	pathnode->path.parallel_aware = false;
-	/* A MinMaxAggPath implies use of subplans, so cannot be parallel-safe */
+	/* A MinMaxAggPath implies use of initplans, so cannot be parallel-safe */
 	pathnode->path.parallel_safe = false;
 	pathnode->path.parallel_workers = 0;
 	/* Result is one unordered row */