diff --git a/contrib/btree_gist/expected/inet.out b/contrib/btree_gist/expected/inet.out
index c323d903da..f15f1435f0 100644
--- a/contrib/btree_gist/expected/inet.out
+++ b/contrib/btree_gist/expected/inet.out
@@ -83,13 +83,13 @@ 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)
+-- this can be an index-only scan, as long as the planner uses the right column
 EXPLAIN (COSTS OFF)
 SELECT count(*) FROM inettmp WHERE a  = '89.225.196.191'::inet;
-                     QUERY PLAN                     
-----------------------------------------------------
+                       QUERY PLAN                        
+---------------------------------------------------------
  Aggregate
-   ->  Index Scan using inettmp_a_a1_idx on inettmp
+   ->  Index Only Scan using inettmp_a_a1_idx on inettmp
          Index Cond: (a = '89.225.196.191'::inet)
 (3 rows)
 
diff --git a/contrib/btree_gist/sql/inet.sql b/contrib/btree_gist/sql/inet.sql
index 4b8d354b00..249e8085c3 100644
--- a/contrib/btree_gist/sql/inet.sql
+++ b/contrib/btree_gist/sql/inet.sql
@@ -42,7 +42,7 @@ DROP INDEX inetidx;
 
 CREATE INDEX ON inettmp USING gist (a gist_inet_ops, a inet_ops);
 
--- likewise here (checks for core planner bug)
+-- this can be an index-only scan, as long as the planner uses the right column
 EXPLAIN (COSTS OFF)
 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 0e4e00eaf0..e2def356f6 100644
--- a/src/backend/optimizer/path/indxpath.c
+++ b/src/backend/optimizer/path/indxpath.c
@@ -1807,7 +1807,6 @@ 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;
 
@@ -1847,11 +1846,7 @@ check_index_only(RelOptInfo *rel, IndexOptInfo *index)
 
 	/*
 	 * Construct a bitmapset of columns that the index can return back in an
-	 * 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.)
+	 * index-only scan.
 	 */
 	for (i = 0; i < index->ncolumns; i++)
 	{
@@ -1868,21 +1863,13 @@ 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;
 }