I've found charging a fixed fee for an agreed upon deliverable to be so utterly BS-free, that it's worth dealing with the smaller problems. The clients love it, because it takes a lot of the risk and possibility that they might be getting shafted out of the equation. I love it because I don't have to justify how I spend the time.

I've found the best solution on my end is simply to first try to estimate a little pessimistically, and then to charge enough that I'll feel fine even if the project takes me a couple days longer than I thought. If a totally unexpected pitfall appears, a reasonable client will be open to renegotiating.

It's so worth it just to avoid the not-so-goodwill that seems to accompany hourly billing so often.