This paper addresses the problem in which jobs of different types arrive at a system that consists of a collection of individual and somewhat diverse processors. The processors differ in that each may spedalize in one job type, but may also do others. Job types that are totally incompatible with a processor have an infinite service on that processor, but degrees of incompatibility may exist, and are modeled here. Using static queuing models, several practical performance measures may be evaluated, and optimal allocation of jobs to processors are obtained by solving linear and nonlinear programming problems. To illustrate, several numerical examples are provided. It is shown that jobs are not always most advantageously assigned to their most expert servers.