I have been working as a freelancer for a few months, providing R&D services for small companies. My preferred mode of collaboration is billing per project, which usually lasts a few weeks. It gives me the flexibility to solve the problems as a want and in the order that I prefer. The disadvantage is that I systematically under-estimate the time required for accomplishing a project, and consequently find myself underpaid.
I have tried for about a month charging per week, but it seems to provoke the dynamics where I am more concerned with showing my client that I do work than focusing on getting good results. Specifically, I avoid the risks of trying new ways that may potentially take a lot of time without certain positive outcome, and I feel pressure from my client to report on the intermediate steps rather then on the final outcome.
I am looking for suggestions on improving collaboration, as well as for the pros and cons of different modes of collaboration that I might not have considered.