Data were provided by the Peoria, Illinois, and Hartford, Connecticut, police departments; the calls were broken down by hour intervals over a 1-week period. The calculations used here demonstrate that a differential response strategy can substantially reduce the total expected cost of delays in a police response system, thus more efficiently allocating resources than on a first-come, first-served basis. The gradient search method used here will find the optimal set of cutoffs with many fewer iterations than previous models. Results of simulated exercises show that the optimal cutoffs are more sensitive to changes in relative workloads in situations where the probability of needing two cars varied across priority groups. The practical implication of the research is that a simple differential response strategy can maximize resources, while a system that uses a computer algorithm to calculate the optimal number of units to hold back will improve efficiency even more. 6 tables, 3 figures,