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The performance of message-passing applications depends on cpu speed, communication throughput and latency, and message handling overhead. In this paper we investigate the effect of varying these parameters and applying techniques to reduce message handling overhead on the execution efficiency of ten different applications. Using a message level simulator set up for the architecture of the AP1000, we showed that improving communication performance, especially message handling, improves total performance. If a cpu that is 32 times faster is provided, the total performance increases by less than ten times unless message handling overhead is reduced. Overlapping computation with message reception improves performance significantly. We also discuss how to improve the AP1000 architecture.