I had the same problem starting out and have smallish hands also.
Get straps. I found that actually strengthened my grip. Why? Not sure. However, the grip muscles are a weird bunch and don't need anything near max effort to develop, I think something like 65-75% of your max effort on grip will develop it just as well as max effort.
So using straps, which decreases the effort of your grip, yet allows you to do more deadlifts etc.. (and, in fact, heavier ones) is probably what did the trick.
I also found that both hands overhand worked better than mixed grip. Go figure!
Hooking your thumb over your index finger helps a lot too.
Obviously if slipping due to sweat etc.. then chalk, gloves, better knurling on bar can all help. Also, get a bike tire inner tube, cut it up, make some rubber squares to wrap around the bar, works real nice if you wrap it the RIGHT way (not so it unwraps when you hold it).
I don't agree with "deadlifts to improve grip" - if your grip lets your deadlift down, then focus on grip until it is good enough. Deadlifts are not the most efficient way. Thick handled, one handed holds are better. There are many other better ways to get grip up to speed. In meantime, don't sacrifice the benefits of deadlifts by not using straps.
I like the Ironmind straps the best they are great, self adjusting etc.... and can be released, and damned strong.