diff --git a/contrib/btree_gist/expected/inet.out b/contrib/btree_gist/expected/inet.out
index 721a78e701..905f55d740 100644
--- a/contrib/btree_gist/expected/inet.out
+++ b/contrib/btree_gist/expected/inet.out
@@ -64,3 +64,42 @@ SELECT count(*) FROM inettmp WHERE a >  '89.225.196.191'::inet;
    386
 (1 row)
 
+VACUUM inettmp;
+-- gist_inet_ops lacks a fetch function, so this should not be index-only scan
+EXPLAIN (COSTS OFF)
+SELECT count(*) FROM inettmp WHERE a  = '89.225.196.191'::inet;
+                       QUERY PLAN                       
+--------------------------------------------------------
+ Aggregate
+   ->  Bitmap Heap Scan on inettmp
+         Recheck Cond: (a = '89.225.196.191'::inet)
+         ->  Bitmap Index Scan on inetidx
+               Index Cond: (a = '89.225.196.191'::inet)
+(5 rows)
+
+SELECT count(*) FROM inettmp WHERE a  = '89.225.196.191'::inet;
+ count 
+-------
+     1
+(1 row)
+
+DROP INDEX inetidx;
+CREATE INDEX ON inettmp USING gist (a gist_inet_ops, a inet_ops);
+-- likewise here (checks for core planner bug)
+EXPLAIN (COSTS OFF)
+SELECT count(*) FROM inettmp WHERE a  = '89.225.196.191'::inet;
+                       QUERY PLAN                       
+--------------------------------------------------------
+ Aggregate
+   ->  Bitmap Heap Scan on inettmp
+         Recheck Cond: (a = '89.225.196.191'::inet)
+         ->  Bitmap Index Scan on inettmp_a_a1_idx
+               Index Cond: (a = '89.225.196.191'::inet)
+(5 rows)
+
+SELECT count(*) FROM inettmp WHERE a  = '89.225.196.191'::inet;
+ count 
+-------
+     1
+(1 row)
+
diff --git a/contrib/btree_gist/sql/inet.sql b/contrib/btree_gist/sql/inet.sql
index 328846c0a3..08952f2c44 100644
--- a/contrib/btree_gist/sql/inet.sql
+++ b/contrib/btree_gist/sql/inet.sql
@@ -29,3 +29,21 @@ SELECT count(*) FROM inettmp WHERE a  = '89.225.196.191'::inet;
 SELECT count(*) FROM inettmp WHERE a >= '89.225.196.191'::inet;
 
 SELECT count(*) FROM inettmp WHERE a >  '89.225.196.191'::inet;
+
+VACUUM inettmp;
+
+-- gist_inet_ops lacks a fetch function, so this should not be index-only scan
+EXPLAIN (COSTS OFF)
+SELECT count(*) FROM inettmp WHERE a  = '89.225.196.191'::inet;
+
+SELECT count(*) FROM inettmp WHERE a  = '89.225.196.191'::inet;
+
+DROP INDEX inetidx;
+
+CREATE INDEX ON inettmp USING gist (a gist_inet_ops, a inet_ops);
+
+-- likewise here (checks for core planner bug)
+EXPLAIN (COSTS OFF)
+SELECT count(*) FROM inettmp WHERE a  = '89.225.196.191'::inet;
+
+SELECT count(*) FROM inettmp WHERE a  = '89.225.196.191'::inet;
diff --git a/src/backend/optimizer/path/indxpath.c b/src/backend/optimizer/path/indxpath.c
index 2952bfb7c2..47a01b3ad0 100644
--- a/src/backend/optimizer/path/indxpath.c
+++ b/src/backend/optimizer/path/indxpath.c
@@ -1791,6 +1791,7 @@ check_index_only(RelOptInfo *rel, IndexOptInfo *index)
 	bool		result;
 	Bitmapset  *attrs_used = NULL;
 	Bitmapset  *index_canreturn_attrs = NULL;
+	Bitmapset  *index_cannotreturn_attrs = NULL;
 	ListCell   *lc;
 	int			i;
 
@@ -1830,7 +1831,11 @@ check_index_only(RelOptInfo *rel, IndexOptInfo *index)
 
 	/*
 	 * Construct a bitmapset of columns that the index can return back in an
-	 * index-only scan.
+	 * index-only scan.  If there are multiple index columns containing the
+	 * same attribute, all of them must be capable of returning the value,
+	 * since we might recheck operators on any of them.  (Potentially we could
+	 * be smarter about that, but it's such a weird situation that it doesn't
+	 * seem worth spending a lot of sweat on.)
 	 */
 	for (i = 0; i < index->ncolumns; i++)
 	{
@@ -1847,13 +1852,21 @@ check_index_only(RelOptInfo *rel, IndexOptInfo *index)
 			index_canreturn_attrs =
 				bms_add_member(index_canreturn_attrs,
 							   attno - FirstLowInvalidHeapAttributeNumber);
+		else
+			index_cannotreturn_attrs =
+				bms_add_member(index_cannotreturn_attrs,
+							   attno - FirstLowInvalidHeapAttributeNumber);
 	}
 
+	index_canreturn_attrs = bms_del_members(index_canreturn_attrs,
+											index_cannotreturn_attrs);
+
 	/* Do we have all the necessary attributes? */
 	result = bms_is_subset(attrs_used, index_canreturn_attrs);
 
 	bms_free(attrs_used);
 	bms_free(index_canreturn_attrs);
+	bms_free(index_cannotreturn_attrs);
 
 	return result;
 }