diff --git a/src/backend/optimizer/prep/prepjointree.c b/src/backend/optimizer/prep/prepjointree.c
index 688b3a1c39..cd6e11904e 100644
--- a/src/backend/optimizer/prep/prepjointree.c
+++ b/src/backend/optimizer/prep/prepjointree.c
@@ -2044,6 +2044,18 @@ replace_vars_in_jointree(Node *jtnode,
 		}
 		replace_vars_in_jointree(j->larg, context, lowest_nulling_outer_join);
 		replace_vars_in_jointree(j->rarg, context, lowest_nulling_outer_join);
+
+		/*
+		 * Use PHVs within the join quals of a full join, even when it's the
+		 * lowest nulling outer join.  Otherwise, we cannot identify which
+		 * side of the join a pulled-up var-free expression came from, which
+		 * can lead to failure to make a plan at all because none of the quals
+		 * appear to be mergeable or hashable conditions.  For this purpose we
+		 * don't care about the state of wrap_non_vars, so leave it alone.
+		 */
+		if (j->jointype == JOIN_FULL)
+			context->need_phvs = true;
+
 		j->quals = pullup_replace_vars(j->quals, context);
 
 		/*
diff --git a/src/test/regress/expected/join.out b/src/test/regress/expected/join.out
index dc6262be43..1f5378080d 100644
--- a/src/test/regress/expected/join.out
+++ b/src/test/regress/expected/join.out
@@ -2024,6 +2024,20 @@ NATURAL FULL JOIN
  ee   |      |   42 |    2 |     
 (4 rows)
 
+-- Constants as join keys can also be problematic
+SELECT * FROM
+  (SELECT name, n as s1_n FROM t1) as s1
+FULL JOIN
+  (SELECT name, 2 as s2_n FROM t2) as s2
+ON (s1_n = s2_n);
+ name | s1_n | name | s2_n 
+------+------+------+------
+      |      | bb   |    2
+      |      | cc   |    2
+      |      | ee   |    2
+ bb   |   11 |      |     
+(4 rows)
+
 -- Test for propagation of nullability constraints into sub-joins
 create temp table x (x1 int, x2 int);
 insert into x values (1,11);
@@ -2854,7 +2868,7 @@ SELECT qq, unique1
 ---------------------------------------------------------------------------------------------------------
  Nested Loop
    ->  Hash Full Join
-         Hash Cond: (COALESCE(a.q1, '0'::bigint) = COALESCE(b.q2, '-1'::bigint))
+         Hash Cond: ((COALESCE(a.q1, '0'::bigint)) = (COALESCE(b.q2, '-1'::bigint)))
          ->  Seq Scan on int8_tbl a
          ->  Hash
                ->  Seq Scan on int8_tbl b
diff --git a/src/test/regress/sql/join.sql b/src/test/regress/sql/join.sql
index d3ba2a1c33..334a4dce2d 100644
--- a/src/test/regress/sql/join.sql
+++ b/src/test/regress/sql/join.sql
@@ -297,6 +297,13 @@ NATURAL FULL JOIN
     (SELECT name, n as s3_n FROM t3) as s3
   ) ss2;
 
+-- Constants as join keys can also be problematic
+SELECT * FROM
+  (SELECT name, n as s1_n FROM t1) as s1
+FULL JOIN
+  (SELECT name, 2 as s2_n FROM t2) as s2
+ON (s1_n = s2_n);
+
 
 -- Test for propagation of nullability constraints into sub-joins