Sorting on notice.id when our primary selector was notice_inbox.user_id caused a filesort and table scan of the notice table.
Switchng to notice_inbox's notice_id means we can use our index, and everything comes right up.
Before:
mysql> explain SELECT notice.id AS id FROM notice JOIN notice_inbox ON notice.id = notice_inbox.notice_id WHERE notice_inbox.user_id = 18574 AND notice.repeat_of IS NULL ORDER BY notice.id DESC LIMIT 61 OFFSET 0;
+----+-------------+--------------+--------+------------------------------------+---------+---------+-------------------------------+--------+----------------------------------------------+
| id | select_type | table | type | possible_keys | key | key_len | ref | rows | Extra |
+----+-------------+--------------+--------+------------------------------------+---------+---------+-------------------------------+--------+----------------------------------------------+
| 1 | SIMPLE | notice_inbox | ref | PRIMARY,notice_inbox_notice_id_idx | PRIMARY | 4 | const | 102600 | Using index; Using temporary; Using filesort |
| 1 | SIMPLE | notice | eq_ref | PRIMARY | PRIMARY | 4 | stoica.notice_inbox.notice_id | 1 | Using index |
+----+-------------+--------------+--------+------------------------------------+---------+---------+-------------------------------+--------+----------------------------------------------+
After:
mysql> explain SELECT notice.id AS id FROM notice JOIN notice_inbox ON notice.id = notice_inbox.notice_id WHERE notice_inbox.user_id = 18574 AND notice.repeat_of IS NULL ORDER BY notice_id DESC LIMIT 61 OFFSET 0;
+----+-------------+--------------+--------+------------------------------------+---------+---------+-------------------------------+--------+--------------------------+
| id | select_type | table | type | possible_keys | key | key_len | ref | rows | Extra |
+----+-------------+--------------+--------+------------------------------------+---------+---------+-------------------------------+--------+--------------------------+
| 1 | SIMPLE | notice_inbox | ref | PRIMARY,notice_inbox_notice_id_idx | PRIMARY | 4 | const | 102816 | Using where; Using index |
| 1 | SIMPLE | notice | eq_ref | PRIMARY,notice_repeatof_idx | PRIMARY | 4 | stoica.notice_inbox.notice_id | 1 | Using where |
+----+-------------+--------------+--------+------------------------------------+---------+---------+-------------------------------+--------+--------------------------+
