A well-established approach to the verification of end-to-end response times for distributed, hard real-time systems is an integrated scheduling analysis of both task processing and message communication. Hitherto, published analyses have been confined to the computation of worst-case bounds only and best-case response times have been ignored, assumed to be zero or treated approximately. However, there are compelling reasons for computing both upper and lower bounds on response times, not only to allow the verification of best-case performance but also to improve the accuracy of the overall analysis. This paper describes a precise best-case execution time analysis which reduces jitter and extends distributed scheduling analysis to yield more accurate upper and lower bounds on system response times. The analysis is combined with existing results for worst-case responses in a single scheduling algorithm to compute both upper and lower bounds on end-to-end response in distributed systems. A design tool has been developed to automate the analysis and support the performance verification of diverse real-time systems composed of tasks executing on multiple processors which communicate using the Controller Area Network (CAN) fieldbus.