diff --git a/contrib/postgres_fdw/expected/postgres_fdw.out b/contrib/postgres_fdw/expected/postgres_fdw.out
index 558e94b845..c07280d836 100644
--- a/contrib/postgres_fdw/expected/postgres_fdw.out
+++ b/contrib/postgres_fdw/expected/postgres_fdw.out
@@ -11377,19 +11377,19 @@ CREATE FOREIGN TABLE foreign_tbl2 () INHERITS (foreign_tbl)
   SERVER loopback OPTIONS (table_name 'base_tbl');
 EXPLAIN (VERBOSE, COSTS OFF)
 SELECT a FROM base_tbl WHERE a IN (SELECT a FROM foreign_tbl);
-                                 QUERY PLAN                                  
------------------------------------------------------------------------------
- Seq Scan on public.base_tbl
+                                QUERY PLAN                                 
+---------------------------------------------------------------------------
+ Nested Loop Semi Join
    Output: base_tbl.a
-   Filter: (SubPlan 1)
-   SubPlan 1
-     ->  Result
-           Output: base_tbl.a
-           ->  Append
-                 ->  Async Foreign Scan on public.foreign_tbl foreign_tbl_1
-                       Remote SQL: SELECT NULL FROM public.base_tbl
-                 ->  Async Foreign Scan on public.foreign_tbl2 foreign_tbl_2
-                       Remote SQL: SELECT NULL FROM public.base_tbl
+   ->  Seq Scan on public.base_tbl
+         Output: base_tbl.a, base_tbl.b
+         Filter: (base_tbl.a IS NOT NULL)
+   ->  Materialize
+         ->  Append
+               ->  Async Foreign Scan on public.foreign_tbl foreign_tbl_1
+                     Remote SQL: SELECT NULL FROM public.base_tbl
+               ->  Async Foreign Scan on public.foreign_tbl2 foreign_tbl_2
+                     Remote SQL: SELECT NULL FROM public.base_tbl
 (11 rows)
 
 SELECT a FROM base_tbl WHERE a IN (SELECT a FROM foreign_tbl);
diff --git a/src/backend/optimizer/plan/subselect.c b/src/backend/optimizer/plan/subselect.c
index 92e3338584..3d4645a154 100644
--- a/src/backend/optimizer/plan/subselect.c
+++ b/src/backend/optimizer/plan/subselect.c
@@ -1271,6 +1271,7 @@ convert_ANY_sublink_to_join(PlannerInfo *root, SubLink *sublink,
 	JoinExpr   *result;
 	Query	   *parse = root->parse;
 	Query	   *subselect = (Query *) sublink->subselect;
+	bool		has_level_1_vars;
 	Relids		upper_varnos;
 	int			rtindex;
 	ParseNamespaceItem *nsitem;
@@ -1283,11 +1284,10 @@ convert_ANY_sublink_to_join(PlannerInfo *root, SubLink *sublink,
 	Assert(sublink->subLinkType == ANY_SUBLINK);
 
 	/*
-	 * The sub-select must not refer to any Vars of the parent query. (Vars of
-	 * higher levels should be okay, though.)
+	 * If the sub-select refers to any Vars of the parent query, we have to
+	 * treat it as LATERAL.  (Vars of higher levels don't matter here.)
 	 */
-	if (contain_vars_of_level((Node *) subselect, 1))
-		return NULL;
+	has_level_1_vars = contain_vars_of_level((Node *) subselect, 1);
 
 	/*
 	 * The test expression must contain some Vars of the parent query, else
@@ -1324,7 +1324,7 @@ convert_ANY_sublink_to_join(PlannerInfo *root, SubLink *sublink,
 	nsitem = addRangeTableEntryForSubquery(pstate,
 										   subselect,
 										   makeAlias("ANY_subquery", NIL),
-										   false,
+										   has_level_1_vars,
 										   false);
 	rte = nsitem->p_rte;
 	parse->rtable = lappend(parse->rtable, rte);
diff --git a/src/test/regress/expected/join.out b/src/test/regress/expected/join.out
index 9358371072..cdaedb92b2 100644
--- a/src/test/regress/expected/join.out
+++ b/src/test/regress/expected/join.out
@@ -4657,17 +4657,17 @@ explain (costs off)
 select a.unique1, b.unique2
   from onek a left join onek b on a.unique1 = b.unique2
   where b.unique2 = any (select q1 from int8_tbl c where c.q1 < b.unique1);
-                        QUERY PLAN                        
-----------------------------------------------------------
- Hash Join
-   Hash Cond: (b.unique2 = a.unique1)
-   ->  Seq Scan on onek b
-         Filter: (SubPlan 1)
-         SubPlan 1
-           ->  Seq Scan on int8_tbl c
-                 Filter: (q1 < b.unique1)
-   ->  Hash
-         ->  Index Only Scan using onek_unique1 on onek a
+                     QUERY PLAN                     
+----------------------------------------------------
+ Nested Loop
+   ->  Hash Semi Join
+         Hash Cond: (b.unique2 = c.q1)
+         Join Filter: (c.q1 < b.unique1)
+         ->  Seq Scan on onek b
+         ->  Hash
+               ->  Seq Scan on int8_tbl c
+   ->  Index Only Scan using onek_unique1 on onek a
+         Index Cond: (unique1 = b.unique2)
 (9 rows)
 
 select a.unique1, b.unique2
@@ -6074,8 +6074,8 @@ lateral (select * from int8_tbl t1,
                                      where q2 = (select greatest(t1.q1,t2.q2))
                                        and (select v.id=0)) offset 0) ss2) ss
          where t1.q1 = ss.q2) ss0;
-                           QUERY PLAN                            
------------------------------------------------------------------
+                             QUERY PLAN                              
+---------------------------------------------------------------------
  Nested Loop
    Output: "*VALUES*".column1, t1.q1, t1.q2, ss2.q1, ss2.q2
    ->  Seq Scan on public.int8_tbl t1
@@ -6087,23 +6087,24 @@ lateral (select * from int8_tbl t1,
          ->  Subquery Scan on ss2
                Output: ss2.q1, ss2.q2
                Filter: (t1.q1 = ss2.q2)
-               ->  Seq Scan on public.int8_tbl t2
+               ->  Result
                      Output: t2.q1, t2.q2
-                     Filter: (SubPlan 3)
-                     SubPlan 3
+                     One-Time Filter: $3
+                     InitPlan 2 (returns $3)
                        ->  Result
-                             Output: t3.q2
-                             One-Time Filter: $4
-                             InitPlan 1 (returns $2)
-                               ->  Result
-                                     Output: GREATEST($0, t2.q2)
-                             InitPlan 2 (returns $4)
-                               ->  Result
-                                     Output: ($3 = 0)
-                             ->  Seq Scan on public.int8_tbl t3
-                                   Output: t3.q1, t3.q2
-                                   Filter: (t3.q2 = $2)
-(27 rows)
+                             Output: ($2 = 0)
+                     ->  Nested Loop Semi Join
+                           Output: t2.q1, t2.q2
+                           Join Filter: (t2.q1 = t3.q2)
+                           ->  Seq Scan on public.int8_tbl t2
+                                 Output: t2.q1, t2.q2
+                                 Filter: ((SubPlan 1) = t2.q1)
+                                 SubPlan 1
+                                   ->  Result
+                                         Output: GREATEST($0, t2.q2)
+                           ->  Seq Scan on public.int8_tbl t3
+                                 Output: t3.q1, t3.q2
+(28 rows)
 
 select * from (values (0), (1)) v(id),
 lateral (select * from int8_tbl t1,