My contractor for my current fix up has been happy with being paid weekly for the jobs he has done, our contract has all the specific tasks listed out with prices for each. I meet him once a week and we go through what is completed, and what he is doing next, sometimes we find another project that needs to be done (fix the hole in the bathroom floor that we found when we moved the tub over). I haven't had any problems with this system, he did ask me for some money for materials before he goes out to buy the paint, but everything else he hasn't required anything upfront. I have worked with several other contractors, most of them want a small amount for materials and then payment at completion for the rest of the work, but I think on a longer job, the weekly payments make more sense.
I also have been able to build up trust between myself and my contractors, I can call them and make add something else and they can get started without a contract in writing, then I just sign something the next time I see them, or just pay if the work is completed.
I am pretty new to this whole thing, but it seems to be working so far.