In a distributed processing system with the application software partitioned into a set of program modules, allocation of those modules to the processors is an important problem. This paper presents a method for optimal module allocation that satisfies certain performance constraints. An objective function that includes the intermodule communication (IMC) and accumulative execution time (AET) of each module is proposed. It minimizes the bottleneck-processor utilization—a good principle for task allocation. Next, the effects of precedence relationship (PR) among program modules on response time are studied. Both simulation and analytical results reveal that the program-size ratio between two consecutive modules plays an important role in task response time. Finally, an algorithm based on PR, AET, and IMC and on the proposed objective function is presented. This algorithm generates better module assignments than those that do not consider the PR effects.