diff --git a/src/backend/parser/parse_cte.c b/src/backend/parser/parse_cte.c
index 6826d4f36a..17432e9df6 100644
--- a/src/backend/parser/parse_cte.c
+++ b/src/backend/parser/parse_cte.c
@@ -877,6 +877,25 @@ checkWellFormedRecursion(CteState *cstate)
 							cte->ctename),
 					 parser_errposition(cstate->pstate, cte->location)));
 
+		/*
+		 * Really, we should insist that there not be a top-level WITH, since
+		 * syntactically that would enclose the UNION.  However, we've not
+		 * done so in the past and it's probably too late to change.  Settle
+		 * for insisting that WITH not contain a self-reference.  Test this
+		 * before examining the UNION arms, to avoid issuing confusing errors
+		 * in such cases.
+		 */
+		if (stmt->withClause)
+		{
+			cstate->curitem = i;
+			cstate->innerwiths = NIL;
+			cstate->selfrefcount = 0;
+			cstate->context = RECURSION_SUBLINK;
+			checkWellFormedRecursionWalker((Node *) stmt->withClause->ctes,
+										   cstate);
+			Assert(cstate->innerwiths == NIL);
+		}
+
 		/* The left-hand operand mustn't contain self-reference at all */
 		cstate->curitem = i;
 		cstate->innerwiths = NIL;
@@ -895,18 +914,6 @@ checkWellFormedRecursion(CteState *cstate)
 		if (cstate->selfrefcount != 1)	/* shouldn't happen */
 			elog(ERROR, "missing recursive reference");
 
-		/* WITH mustn't contain self-reference, either */
-		if (stmt->withClause)
-		{
-			cstate->curitem = i;
-			cstate->innerwiths = NIL;
-			cstate->selfrefcount = 0;
-			cstate->context = RECURSION_SUBLINK;
-			checkWellFormedRecursionWalker((Node *) stmt->withClause->ctes,
-										   cstate);
-			Assert(cstate->innerwiths == NIL);
-		}
-
 		/*
 		 * Disallow ORDER BY and similar decoration atop the UNION. These
 		 * don't make sense because it's impossible to figure out what they
diff --git a/src/test/regress/expected/with.out b/src/test/regress/expected/with.out
index b4f3121751..fff2d4949e 100644
--- a/src/test/regress/expected/with.out
+++ b/src/test/regress/expected/with.out
@@ -2029,6 +2029,38 @@ WITH RECURSIVE x(n) AS (SELECT n FROM x UNION ALL SELECT 1)
 ERROR:  recursive reference to query "x" must not appear within its non-recursive term
 LINE 1: WITH RECURSIVE x(n) AS (SELECT n FROM x UNION ALL SELECT 1)
                                               ^
+-- allow this, because we historically have
+WITH RECURSIVE x(n) AS (
+  WITH x1 AS (SELECT 1 AS n)
+    SELECT 0
+    UNION
+    SELECT * FROM x1)
+	SELECT * FROM x;
+ n 
+---
+ 0
+ 1
+(2 rows)
+
+-- but this should be rejected
+WITH RECURSIVE x(n) AS (
+  WITH x1 AS (SELECT 1 FROM x)
+    SELECT 0
+    UNION
+    SELECT * FROM x1)
+	SELECT * FROM x;
+ERROR:  recursive reference to query "x" must not appear within a subquery
+LINE 2:   WITH x1 AS (SELECT 1 FROM x)
+                                    ^
+-- and this too
+WITH RECURSIVE x(n) AS (
+  (WITH x1 AS (SELECT 1 FROM x) SELECT * FROM x1)
+  UNION
+  SELECT 0)
+	SELECT * FROM x;
+ERROR:  recursive reference to query "x" must not appear within its non-recursive term
+LINE 2:   (WITH x1 AS (SELECT 1 FROM x) SELECT * FROM x1)
+                                     ^
 CREATE TEMPORARY TABLE y (a INTEGER);
 INSERT INTO y SELECT generate_series(1, 10);
 -- LEFT JOIN
diff --git a/src/test/regress/sql/with.sql b/src/test/regress/sql/with.sql
index 3fb0b33fce..06b2d4857f 100644
--- a/src/test/regress/sql/with.sql
+++ b/src/test/regress/sql/with.sql
@@ -908,6 +908,29 @@ WITH RECURSIVE x(n) AS (SELECT n FROM x)
 WITH RECURSIVE x(n) AS (SELECT n FROM x UNION ALL SELECT 1)
 	SELECT * FROM x;
 
+-- allow this, because we historically have
+WITH RECURSIVE x(n) AS (
+  WITH x1 AS (SELECT 1 AS n)
+    SELECT 0
+    UNION
+    SELECT * FROM x1)
+	SELECT * FROM x;
+
+-- but this should be rejected
+WITH RECURSIVE x(n) AS (
+  WITH x1 AS (SELECT 1 FROM x)
+    SELECT 0
+    UNION
+    SELECT * FROM x1)
+	SELECT * FROM x;
+
+-- and this too
+WITH RECURSIVE x(n) AS (
+  (WITH x1 AS (SELECT 1 FROM x) SELECT * FROM x1)
+  UNION
+  SELECT 0)
+	SELECT * FROM x;
+
 CREATE TEMPORARY TABLE y (a INTEGER);
 INSERT INTO y SELECT generate_series(1, 10);