The reverse 21 method works really well for chin-ups and can be modified to fit your current ability level. It's rare to find people who can crank out 21 good chin-ups, but if you can do 15, then you should be able to do reverse 21s. It's a great way to pound your lats and upper back.
- Start with full reps.
- Then do top-half partials where you start with your upper arms parallel to the floor and pull yourself all the way up.
- Finish with bottom-range partials where you start with your arms fully extended and pull up until your upper arms are about parallel to the floor.
If 21 total reps is too tough, adjust accordingly. Even if you're doing 2-3 reps per mini-set, it's still a great way to hit your back. Lat pulldowns also work well, but rowing variations don't work as well. Stick to vertical pulling exercises.