diff --git a/src/backend/optimizer/plan/setrefs.c b/src/backend/optimizer/plan/setrefs.c
index 61d3c6842c..1dc956c3f0 100644
--- a/src/backend/optimizer/plan/setrefs.c
+++ b/src/backend/optimizer/plan/setrefs.c
@@ -1350,8 +1350,16 @@ set_append_references(PlannerInfo *root,
 		lfirst(l) = set_plan_refs(root, (Plan *) lfirst(l), rtoffset);
 	}
 
-	/* Now, if there's just one, forget the Append and return that child */
-	if (list_length(aplan->appendplans) == 1)
+	/*
+	 * See if it's safe to get rid of the Append entirely.  For this to be
+	 * safe, there must be only one child plan and that child plan's parallel
+	 * awareness must match that of the Append's.  The reason for the latter
+	 * is that the if the Append is parallel aware and the child is not then
+	 * the calling plan may execute the non-parallel aware child multiple
+	 * times.
+	 */
+	if (list_length(aplan->appendplans) == 1 &&
+		((Plan *) linitial(aplan->appendplans))->parallel_aware == aplan->plan.parallel_aware)
 		return clean_up_removed_plan_level((Plan *) aplan,
 										   (Plan *) linitial(aplan->appendplans));
 
@@ -1412,8 +1420,16 @@ set_mergeappend_references(PlannerInfo *root,
 		lfirst(l) = set_plan_refs(root, (Plan *) lfirst(l), rtoffset);
 	}
 
-	/* Now, if there's just one, forget the MergeAppend and return that child */
-	if (list_length(mplan->mergeplans) == 1)
+	/*
+	 * See if it's safe to get rid of the MergeAppend entirely.  For this to
+	 * be safe, there must be only one child plan and that child plan's
+	 * parallel awareness must match that of the MergeAppend's.  The reason
+	 * for the latter is that the if the MergeAppend is parallel aware and the
+	 * child is not then the calling plan may execute the non-parallel aware
+	 * child multiple times.
+	 */
+	if (list_length(mplan->mergeplans) == 1 &&
+		((Plan *) linitial(mplan->mergeplans))->parallel_aware == mplan->plan.parallel_aware)
 		return clean_up_removed_plan_level((Plan *) mplan,
 										   (Plan *) linitial(mplan->mergeplans));