Comment 2 for bug 1324405

This is easy to confirm with PS 5.6.17:

openxs@ao756:~/dbs/p5.6$ mysql -uroot -proot test
Warning: Using a password on the command line interface can be insecure.
Reading table information for completion of table and column names
You can turn off this feature to get a quicker startup with -A

Welcome to the MySQL monitor. Commands end with ; or \g.
Your MySQL connection id is 1
Server version: 5.6.17-65.0-587.saucy (Ubuntu)

Copyright (c) 2009-2014 Percona LLC and/or its affiliates
Copyright (c) 2000, 2014, Oracle and/or its affiliates. All rights reserved.

Oracle is a registered trademark of Oracle Corporation and/or its
affiliates. Other names may be trademarks of their respective
owners.

Type 'help;' or '\h' for help. Type '\c' to clear the current input statement.

mysql> CREATE TABLE update_test (a INT AUTO_INCREMENT PRIMARY KEY, b INT, c INT,
    -> INDEX (b,c));
Query OK, 0 rows affected (0,93 sec)

mysql> INSERT INTO update_test (b, c) VALUES (1, 1), (1, 2), (1,3), (2, 2), (2,
    -> 3), (2,4), (2, 5), (5, 5), (6,6), (7,7);
Query OK, 10 rows affected (0,08 sec)
Records: 10 Duplicates: 0 Warnings: 0

mysql> SELECT * FROM update_test WHERE b = 1 ORDER BY c LIMIT 2;
+---+------+------+
| a | b | c |
+---+------+------+
| 1 | 1 | 1 |
| 2 | 1 | 2 |
+---+------+------+
2 rows in set (0,06 sec)

mysql> SHOW SESSION STATUS LIKE 'Sort%';
+-------------------+-------+
| Variable_name | Value |
+-------------------+-------+
| Sort_merge_passes | 0 |
| Sort_range | 0 |
| Sort_rows | 0 |
| Sort_scan | 0 |
+-------------------+-------+
4 rows in set (0,00 sec)

mysql> explain SELECT * FROM update_test WHERE b = 1 ORDER BY c LIMIT 2;
+----+-------------+-------------+------+---------------+------+---------+-------+------+--------------------------+
| id | select_type | table | type | possible_keys | key | key_len | ref | rows | Extra |
+----+-------------+-------------+------+---------------+------+---------+-------+------+--------------------------+
| 1 | SIMPLE | update_test | ref | b | b | 5 | const | 3 | Using where; Using index |
+----+-------------+-------------+------+---------------+------+---------+-------+------+--------------------------+
1 row in set (0,02 sec)

mysql> UPDATE update_test SET a = a + 10 WHERE b = 1 ORDER BY c LIMIT 2;
Query OK, 2 rows affected (0,07 sec)
Rows matched: 2 Changed: 2 Warnings: 0

mysql> SHOW SESSION STATUS LIKE 'Sort%';
+-------------------+-------+
| Variable_name | Value |
+-------------------+-------+
| Sort_merge_passes | 0 |
| Sort_range | 1 |
| Sort_rows | 2 |
| Sort_scan | 0 |
+-------------------+-------+
4 rows in set (0,00 sec)

mysql> explain UPDATE update_test SET a = a + 10 WHERE b = 1 ORDER BY c LIMIT 2;
+----+-------------+-------------+-------+---------------+------+---------+-------+------+-----------------------------+
| id | select_type | table | type | possible_keys | key | key_len | ref | rows | Extra |
+----+-------------+-------------+-------+---------------+------+---------+-------+------+-----------------------------+
| 1 | SIMPLE | update_test | range | b | b | 5 | const | 3 | Using where; Using filesort |
+----+-------------+-------------+-------+---------------+------+---------+-------+------+-----------------------------+
1 row in set (0,00 sec)