In this paper we present improved techniques for the schedulability analysis of tasks with precedence relations in multiprocessor and distributed systems, scheduled under a preemptive fixed priority scheduler. Recently developed techniques, based on the analysis of tasks with dynamic offsets, take into account the precedence relations between tasks only indirectly, through terms iteratively estimated from the response times of the tasks. With the techniques presented in this paper, we exploit the precedence relations in a more accurate way, and we also take advantage of the priority structure of the different tasks. These considerations permit a significant improvement of the results of the analysis applied to distributed and multiprocessor systems.