diff --git a/src/backend/optimizer/plan/initsplan.c b/src/backend/optimizer/plan/initsplan.c
index 904f710d593..2b2c6af9ef8 100644
--- a/src/backend/optimizer/plan/initsplan.c
+++ b/src/backend/optimizer/plan/initsplan.c
@@ -1540,7 +1540,8 @@ make_outerjoininfo(PlannerInfo *root,
 			}
 			else if (jointype == JOIN_LEFT &&
 					 otherinfo->jointype == JOIN_LEFT &&
-					 bms_overlap(strict_relids, otherinfo->min_righthand))
+					 bms_overlap(strict_relids, otherinfo->min_righthand) &&
+					 !bms_overlap(clause_relids, otherinfo->syn_lefthand))
 			{
 				/* Identity 3 applies, so remove the ordering restriction */
 				min_lefthand = bms_del_member(min_lefthand, otherinfo->ojrelid);
@@ -1985,12 +1986,18 @@ deconstruct_distribute_oj_quals(PlannerInfo *root,
 			/*
 			 * When we are looking at joins above sjinfo, we are envisioning
 			 * pushing sjinfo to above othersj, so add othersj's nulling bit
-			 * before distributing the quals.
+			 * before distributing the quals.  We should add it to Vars coming
+			 * from the current join's LHS: we want to transform the second
+			 * form of OJ identity 3 to the first form, in which Vars of
+			 * relation B will appear nulled by the syntactically-upper OJ
+			 * within the Pbc clause, but those of relation C will not.  (In
+			 * the notation used by optimizer/README, we're converting a qual
+			 * of the form Pbc to Pb*c.)
 			 */
 			if (above_sjinfo)
 				quals = (List *)
 					add_nulling_relids((Node *) quals,
-									   othersj->min_righthand,
+									   sjinfo->syn_lefthand,
 									   bms_make_singleton(othersj->ojrelid));
 
 			/* Compute qualscope and ojscope for this join level */
@@ -2041,12 +2048,16 @@ deconstruct_distribute_oj_quals(PlannerInfo *root,
 			/*
 			 * Adjust qual nulling bits for next level up, if needed.  We
 			 * don't want to put sjinfo's own bit in at all, and if we're
-			 * above sjinfo then we did it already.
+			 * above sjinfo then we did it already.  Here, we should mark all
+			 * Vars coming from the lower join's RHS.  (Again, we are
+			 * converting a qual of the form Pbc to Pb*c, but now we are
+			 * putting back bits that were there in the parser output and were
+			 * temporarily stripped above.)
 			 */
 			if (below_sjinfo)
 				quals = (List *)
 					add_nulling_relids((Node *) quals,
-									   othersj->min_righthand,
+									   othersj->syn_righthand,
 									   bms_make_singleton(othersj->ojrelid));
 
 			/* ... and track joins processed so far */
diff --git a/src/test/regress/expected/join.out b/src/test/regress/expected/join.out
index 75f03fcf30c..98d611412df 100644
--- a/src/test/regress/expected/join.out
+++ b/src/test/regress/expected/join.out
@@ -5068,6 +5068,31 @@ where current_user is not null;  -- this is to add a Result node
                ->  Seq Scan on int4_tbl i4
 (6 rows)
 
+-- and further discussion of bug #17781
+explain (costs off)
+select *
+from int8_tbl t1
+  left join (int8_tbl t2 left join onek t3 on t2.q1 > t3.unique1)
+    on t1.q2 = t2.q2
+  left join onek t4
+    on t2.q2 < t3.unique2;
+                   QUERY PLAN                    
+-------------------------------------------------
+ Nested Loop Left Join
+   Join Filter: (t2.q2 < t3.unique2)
+   ->  Nested Loop Left Join
+         Join Filter: (t2.q1 > t3.unique1)
+         ->  Hash Left Join
+               Hash Cond: (t1.q2 = t2.q2)
+               ->  Seq Scan on int8_tbl t1
+               ->  Hash
+                     ->  Seq Scan on int8_tbl t2
+         ->  Materialize
+               ->  Seq Scan on onek t3
+   ->  Materialize
+         ->  Seq Scan on onek t4
+(13 rows)
+
 -- check that join removal works for a left join when joining a subquery
 -- that is guaranteed to be unique by its GROUP BY clause
 explain (costs off)
diff --git a/src/test/regress/sql/join.sql b/src/test/regress/sql/join.sql
index 2e764cdd51d..e50a7696069 100644
--- a/src/test/regress/sql/join.sql
+++ b/src/test/regress/sql/join.sql
@@ -1820,6 +1820,15 @@ from (select f1/2 as x from int4_tbl i4 left join a on a.id = i4.f1) ss1
      right join int8_tbl i8 on true
 where current_user is not null;  -- this is to add a Result node
 
+-- and further discussion of bug #17781
+explain (costs off)
+select *
+from int8_tbl t1
+  left join (int8_tbl t2 left join onek t3 on t2.q1 > t3.unique1)
+    on t1.q2 = t2.q2
+  left join onek t4
+    on t2.q2 < t3.unique2;
+
 -- check that join removal works for a left join when joining a subquery
 -- that is guaranteed to be unique by its GROUP BY clause
 explain (costs off)