Why do birds rub their bills on branches?

I have often watched birds wiping their beaks back and forth on a branch, and wondered what was going through their minds.
The answer is not exactly rocket science (or even advanced zoology). They mainly do it to clean their bills after eating (and the messier the meal - e.g. berries, juicy insects, suet from a bird-feeder - the more they clean their bills).
But, to some extent, they also do it to shape, sharpen and fine-tune their bills (this was my hypothesis). And, probably to an even lesser extent, it may also be part of marking territory and leaving scent from their "preen oils" (this is hypothesized from the observation that males do it more often and longer when females are around than when just makes are watching).