Existing end-to-end response time analysis in distributed real-time systems , where the finalization of one task on a processor activates another task on another processor, is pes- simistic. By “pessimistic” we mean that not all systems deemed to be unschedulable by the analysis are in fact unschedulable. This pessimism has two causes: (i) the existing analysis is based on best-case response times rather than best-case finalization times and (ii) those best-case response times are based on analysis for (worst-case) deadlines at most equal to periods minus (absolute) activation jitter. In this paper, we present analytical means to determine best-case finalization times of independent real-time tasks with deadlines larger than periods minus activation jitter under uniprocessor fixed-priority preemptive scheduling (FPPS) and arbitrary phasing, allowing an improvement of the existing analysis. We will illustrate the improvement by means of an example.