In this paper, we study the problem of the fixed priority scheduling of hard real-time tasks. We consider independent tasks, which are characterized by a period, a hard deadline, a computation time, and an offset (the time of the first request) where the latter can be chosen by the scheduling algorithm. Considering only the synchronous case is very pessimistic for offset free systems, since the synchronous case is the worst case. An heuristic has been proposed in the past to choose the offsets. In this paper, we propose a new technique, based on the Audsley's priority assignment, to reduce significantly the search space. In addition, we propose new offset assignment heuristics and show the improvement of combining the new technique and the new heuristics.