diff --git a/src/backend/optimizer/path/allpaths.c b/src/backend/optimizer/path/allpaths.c
index 5d7c6abad94..2009ca4acf5 100644
--- a/src/backend/optimizer/path/allpaths.c
+++ b/src/backend/optimizer/path/allpaths.c
@@ -1031,10 +1031,15 @@ get_cheapest_parameterized_child_path(PlannerInfo *root, RelOptInfo *rel,
  * accumulate_append_subpath
  *		Add a subpath to the list being built for an Append or MergeAppend
  *
- * It's possible that the child is itself an Append path, in which case
- * we can "cut out the middleman" and just add its child paths to our
- * own list.  (We don't try to do this earlier because we need to
- * apply both levels of transformation to the quals.)
+ * It's possible that the child is itself an Append or MergeAppend path, in
+ * which case we can "cut out the middleman" and just add its child paths to
+ * our own list.  (We don't try to do this earlier because we need to apply
+ * both levels of transformation to the quals.)
+ *
+ * Note that if we omit a child MergeAppend in this way, we are effectively
+ * omitting a sort step, which seems fine: if the parent is to be an Append,
+ * its result would be unsorted anyway, while if the parent is to be a
+ * MergeAppend, there's no point in a separate sort on a child.
  */
 static List *
 accumulate_append_subpath(List *subpaths, Path *path)
@@ -1046,6 +1051,13 @@ accumulate_append_subpath(List *subpaths, Path *path)
 		/* list_copy is important here to avoid sharing list substructure */
 		return list_concat(subpaths, list_copy(apath->subpaths));
 	}
+	else if (IsA(path, MergeAppendPath))
+	{
+		MergeAppendPath *mpath = (MergeAppendPath *) path;
+
+		/* list_copy is important here to avoid sharing list substructure */
+		return list_concat(subpaths, list_copy(mpath->subpaths));
+	}
 	else
 		return lappend(subpaths, path);
 }
diff --git a/src/backend/optimizer/path/equivclass.c b/src/backend/optimizer/path/equivclass.c
index 257563ce6d1..93ac033ab8b 100644
--- a/src/backend/optimizer/path/equivclass.c
+++ b/src/backend/optimizer/path/equivclass.c
@@ -1937,16 +1937,20 @@ add_child_rel_equivalences(PlannerInfo *root,
 		if (cur_ec->ec_has_volatile)
 			continue;
 
-		/* No point in searching if parent rel not mentioned in eclass */
-		if (!bms_is_subset(parent_rel->relids, cur_ec->ec_relids))
+		/*
+		 * No point in searching if parent rel not mentioned in eclass; but
+		 * we can't tell that for sure if parent rel is itself a child.
+		 */
+		if (parent_rel->reloptkind == RELOPT_BASEREL &&
+			!bms_is_subset(parent_rel->relids, cur_ec->ec_relids))
 			continue;
 
 		foreach(lc2, cur_ec->ec_members)
 		{
 			EquivalenceMember *cur_em = (EquivalenceMember *) lfirst(lc2);
 
-			if (cur_em->em_is_const || cur_em->em_is_child)
-				continue;		/* ignore consts and children here */
+			if (cur_em->em_is_const)
+				continue;		/* ignore consts here */
 
 			/* Does it reference parent_rel? */
 			if (bms_overlap(cur_em->em_relids, parent_rel->relids))
diff --git a/src/backend/optimizer/plan/createplan.c b/src/backend/optimizer/plan/createplan.c
index 46df0daf280..3a54cb14652 100644
--- a/src/backend/optimizer/plan/createplan.c
+++ b/src/backend/optimizer/plan/createplan.c
@@ -753,7 +753,7 @@ create_merge_append_plan(PlannerInfo *root, MergeAppendPath *best_path)
 
 	/* Compute sort column info, and adjust MergeAppend's tlist as needed */
 	(void) prepare_sort_from_pathkeys(root, plan, pathkeys,
-									  NULL,
+									  best_path->path.parent->relids,
 									  NULL,
 									  true,
 									  &node->numCols,
diff --git a/src/test/regress/expected/union.out b/src/test/regress/expected/union.out
index ae690cf9689..c900588c5d9 100644
--- a/src/test/regress/expected/union.out
+++ b/src/test/regress/expected/union.out
@@ -501,9 +501,78 @@ explain (costs off)
                Index Cond: (ab = 'ab'::text)
 (6 rows)
 
+--
+-- Test that ORDER BY for UNION ALL can be pushed down to inheritance
+-- children.
+--
+CREATE TEMP TABLE t1c (b text, a text);
+ALTER TABLE t1c INHERIT t1;
+CREATE TEMP TABLE t2c (primary key (ab)) INHERITS (t2);
+INSERT INTO t1c VALUES ('v', 'w'), ('c', 'd'), ('m', 'n'), ('e', 'f');
+INSERT INTO t2c VALUES ('vw'), ('cd'), ('mn'), ('ef');
+CREATE INDEX t1c_ab_idx on t1c ((a || b));
+set enable_seqscan = on;
+set enable_indexonlyscan = off;
+explain (costs off)
+  SELECT * FROM
+  (SELECT a || b AS ab FROM t1
+   UNION ALL
+   SELECT ab FROM t2) t
+  ORDER BY 1 LIMIT 8;
+                   QUERY PLAN                   
+------------------------------------------------
+ Limit
+   ->  Merge Append
+         Sort Key: ((t1.a || t1.b))
+         ->  Index Scan using t1_ab_idx on t1
+         ->  Index Scan using t1c_ab_idx on t1c
+         ->  Index Scan using t2_pkey on t2
+         ->  Index Scan using t2c_pkey on t2c
+(7 rows)
+
+  SELECT * FROM
+  (SELECT a || b AS ab FROM t1
+   UNION ALL
+   SELECT ab FROM t2) t
+  ORDER BY 1 LIMIT 8;
+ ab 
+----
+ ab
+ ab
+ cd
+ dc
+ ef
+ fe
+ mn
+ nm
+(8 rows)
+
 reset enable_seqscan;
 reset enable_indexscan;
 reset enable_bitmapscan;
+-- This simpler variant of the above test has been observed to fail differently
+create table events (event_id int primary key);
+create table other_events (event_id int primary key);
+create table events_child () inherits (events);
+explain (costs off)
+select event_id
+ from (select event_id from events
+       union all
+       select event_id from other_events) ss
+ order by event_id;
+                        QUERY PLAN                        
+----------------------------------------------------------
+ Merge Append
+   Sort Key: events.event_id
+   ->  Index Scan using events_pkey on events
+   ->  Sort
+         Sort Key: events_child.event_id
+         ->  Seq Scan on events_child
+   ->  Index Scan using other_events_pkey on other_events
+(7 rows)
+
+drop table events_child, events, other_events;
+reset enable_indexonlyscan;
 -- Test constraint exclusion of UNION ALL subqueries
 explain (costs off)
  SELECT * FROM
diff --git a/src/test/regress/sql/union.sql b/src/test/regress/sql/union.sql
index d567cf14819..9ff1551e5de 100644
--- a/src/test/regress/sql/union.sql
+++ b/src/test/regress/sql/union.sql
@@ -198,10 +198,55 @@ explain (costs off)
   SELECT * FROM t2) t
  WHERE ab = 'ab';
 
+--
+-- Test that ORDER BY for UNION ALL can be pushed down to inheritance
+-- children.
+--
+
+CREATE TEMP TABLE t1c (b text, a text);
+ALTER TABLE t1c INHERIT t1;
+CREATE TEMP TABLE t2c (primary key (ab)) INHERITS (t2);
+INSERT INTO t1c VALUES ('v', 'w'), ('c', 'd'), ('m', 'n'), ('e', 'f');
+INSERT INTO t2c VALUES ('vw'), ('cd'), ('mn'), ('ef');
+CREATE INDEX t1c_ab_idx on t1c ((a || b));
+
+set enable_seqscan = on;
+set enable_indexonlyscan = off;
+
+explain (costs off)
+  SELECT * FROM
+  (SELECT a || b AS ab FROM t1
+   UNION ALL
+   SELECT ab FROM t2) t
+  ORDER BY 1 LIMIT 8;
+
+  SELECT * FROM
+  (SELECT a || b AS ab FROM t1
+   UNION ALL
+   SELECT ab FROM t2) t
+  ORDER BY 1 LIMIT 8;
+
 reset enable_seqscan;
 reset enable_indexscan;
 reset enable_bitmapscan;
 
+-- This simpler variant of the above test has been observed to fail differently
+
+create table events (event_id int primary key);
+create table other_events (event_id int primary key);
+create table events_child () inherits (events);
+
+explain (costs off)
+select event_id
+ from (select event_id from events
+       union all
+       select event_id from other_events) ss
+ order by event_id;
+
+drop table events_child, events, other_events;
+
+reset enable_indexonlyscan;
+
 -- Test constraint exclusion of UNION ALL subqueries
 explain (costs off)
  SELECT * FROM