I like the idea, mathematics, and symmetry behind Ethan Reeves "Density" approach to rep related goals. Here's one post on it (scroll down on the linked page):
The idea is this. Fix a rest interval, say 1 minute. Double your number of reps that you want to do. Say I want to get 20 chins. My number is 40 chins. Then, simply start with doubles and do as many sets as necessary to get to the modified rep goal (40). Here, I'd start out with 20x2. When that was "doable" or "moderately easy" ... I'd move to triples. Since 3 doesn't "go into" 40 evenly, I'll use 42 instead. So, now I do 14x3. And so forth:
20 of 2
14 of 3 (42)
10 of 4
8 of 5
7 of 6 (42)
6 of 7 (42)
5 of 8
4 of 10
I think 10 reps, 1 min rest, 10 reps, 1 min rest, 10 reps, 1 min rest, 10 reps will get you really darn close to 20 reps. I can't tell you for certain, b/c I've only played around with this ... though since I rolled my foot (OUCH!), I'm moving to an upper body specialization program and I'm using this progression for chins and dips (with the goal being a muscle-up). If 4 of 10 doesn't do it for you, you could step to 3 of 14.
I'll probably do this twice a week (advancing when the current progression is tolerable) with a third day of heavier stuff thrown in ... 3x3, 5x5, 8x3 or so. Just to keep working on the limit strength as well.