Regularly doing small amounts of pullups was how I got mine up (while AD was 13-16 depending on the year, max during my org's training program was 18-19, max-ever was 26, currently can do 17-18 on demand).
For most, it seems that the hard part is getting to about 5-10 consecutive pullups; after that, they have sufficient ability to condition themselves past that plateau, particularly through circuit routines with a reduction of their max-possible per set.
When I was in my org's training program, I had a pullup bar hung on the bathroom doorframe, and each morning went something like:
Wakeup.
Do 1 pullup.
Piss.
Do 2 pullups.
Drink half the nalgene of water.
Do 3 pullups.
Shave.
Do 4 pullups.
Brush teeth.
Do 5 pullups.
Shower.
Do 4 pullups.
Towel off.
Do 3 pullups.
Socks + boots on.
Do 2 pullups.
Clothes on.
Do 1 pullup.
Gear on, drink the other half of the nalgene, top it off, and leave.