diff --git a/mysql-test/main/explain_non_select.result b/mysql-test/main/explain_non_select.result
index ca8aa246c98..aa3c4787dc7 100644
--- a/mysql-test/main/explain_non_select.result
+++ b/mysql-test/main/explain_non_select.result
@@ -72,7 +72,7 @@ id	select_type	table	type	possible_keys	key	key_len	ref	rows	Extra
 # This should use an index,  possible_keys=NULL because there is no WHERE
 explain update t1 set a=a+1 order by a limit 2;
 id	select_type	table	type	possible_keys	key	key_len	ref	rows	Extra
-1	SIMPLE	t1	ALL	NULL	NULL	NULL	NULL	512	Using filesort
+1	SIMPLE	t1	index	NULL	a	5	NULL	2	Using buffer
 # This should use range, possible_keys={a,b}
 explain update t1 set filler='fooo' where a<20 and b < 10;
 id	select_type	table	type	possible_keys	key	key_len	ref	rows	Extra
diff --git a/mysql-test/main/update.result b/mysql-test/main/update.result
index 57814754e8e..4e5287ab6c8 100644
--- a/mysql-test/main/update.result
+++ b/mysql-test/main/update.result
@@ -288,7 +288,7 @@ update t1 set a=9999 order by a limit 1;
 update t1 set b=9999 order by a limit 1;
 show status like 'handler_read%';
 Variable_name	Value
-Handler_read_first	1
+Handler_read_first	2
 Handler_read_key	0
 Handler_read_last	0
 Handler_read_next	0
@@ -296,7 +296,7 @@ Handler_read_prev	0
 Handler_read_retry	0
 Handler_read_rnd	2
 Handler_read_rnd_deleted	0
-Handler_read_rnd_next	9
+Handler_read_rnd_next	0
 flush status;
 delete from t1 order by a limit 1;
 show status like 'handler_read%';
diff --git a/sql/sql_select.cc b/sql/sql_select.cc
index 5223150ca97..23da54feae0 100644
--- a/sql/sql_select.cc
+++ b/sql/sql_select.cc
@@ -33411,8 +33411,7 @@ uint get_index_for_order(ORDER *order, TABLE *table, SQL_SELECT *select,
     double new_cost;
     if (test_if_cheaper_ordering(FALSE, NULL, order, table,
                                  table->keys_in_use_for_order_by, -1, limit,
-                                 &key, &direction, &limit, &new_cost) &&
-        !is_key_used(table, key, table->write_set))
+                                 &key, &direction, &limit, &new_cost))
     {
       *need_sort= FALSE;
       *scanned_limit= limit;