LOWER() influences utf8_bin collation?

[Wojciech Scigala]

I've encountered a strange behaviour of LOWER() function, which in some way influences sorting behaviour. The database and table are all UTF8, with collation set to utf8_bin. Mysql 5.6.14 on FreeBSD.

Example code:

SET NAMES utf8 COLLATE utf8_bin;
CREATE TABLE t (a varchar(4)) DEFAULT CHARACTER SET 'UTF8' COLLATE 'utf8_bin';
INSERT INTO t VALUES ('zzz');
INSERT INTO t VALUES ('tt');
INSERT INTO t VALUES ('m');
INSERT INTO t VALUES ('kkk');
INSERT INTO t VALUES ('bb');
INSERT INTO t VALUES ('a');

mysql> SELECT a FROM t ORDER BY a;
+------+
| a    |
+------+
| a    |
| bb   |
| kkk  |
| m    |
| tt   |
| zzz  |
+------+

mysql> SELECT a FROM t ORDER BY LOWER(a);
+------+
| a    |
+------+
| m    |
| a    |
| bb   |
| kkk  |
| tt   |
| zzz  |
+------+
6 rows in set (0.00 sec)

While both SELECTs should return exactly same values, they do not. LOWERed results have single-letter values ordered first, I have no idea why. Can somebody shed some light?

PS. I know I can use utf8_general_ci for case-insensitive ordering. I'm not asking for a walkaround solution ;)