Perf of select mysql query is really bad - mysql

Question

I'm not sure why this query is taking 4 minutes to complete:
SELECT
su.sid,u.uid,u.display_name,u.locale
FROM user u
LEFT JOIN subscription_user su ON su.uid = u.uid
ORDER BY u.display_name DESC
LIMIT 0,25;
Well, I know it's due to the order, remove it and it's very fast. If I change to using INNER JOIN instead it's fast but the issue is not all users may be in the subscription_user table.
CREATE TABLE `user` (
`uid` int(11) NOT NULL AUTO_INCREMENT,
`password` varchar(100) DEFAULT NULL,
`user_type` varchar(10) NOT NULL DEFAULT 'user',
`display_name` varchar(50) NOT NULL,
`email` varchar(100) NOT NULL,
`locale` varchar(8) DEFAULT 'en',
`last_login` datetime DEFAULT NULL,
`auth_type` varchar(10) DEFAULT NULL,
`auth_data` varchar(500) DEFAULT NULL,
`inactive` tinyint(4) NOT NULL DEFAULT '0',
`receive_email` tinyint(4) NOT NULL DEFAULT '1',
`stateid` int(10) DEFAULT NULL,
`owner_group_id` int(11) DEFAULT NULL,
`signature` varchar(500) DEFAULT NULL,
`raw_signature` varchar(500) DEFAULT NULL,
`round_robin` smallint(5) unsigned NOT NULL DEFAULT '0',
PRIMARY KEY (`uid`),
UNIQUE KEY `email` (`email`),
KEY `stateid` (`stateid`) USING BTREE,
KEY `user_type` (`user_type`) USING BTREE,
KEY `name` (`display_name`)
) ENGINE=InnoDB AUTO_INCREMENT=28343 DEFAULT CHARSET=latin1;
CREATE TABLE `subscription_user` (
`sid` varchar(50) NOT NULL,
`uid` int(11) NOT NULL,
`deleted` tinyint(4) NOT NULL DEFAULT '0',
`forum_user` varchar(50) NOT NULL,
PRIMARY KEY (`sid`,`uid`)
) ENGINE=InnoDB DEFAULT CHARSET=latin1;

Answer 1

When you have an SQL query, the index can only really help you if the first column in the index is part of the query.
Your query joins su.uid = u.uid and the optimizer will not be able to use that to reference the first column in the subscription primary key index.
You should either reverse the order of the columns in the primary key, or alternatively, you should add a foreign key index, or an independent index on the uid