This method is appropriate for evaluating programs that change the rate of occurrence of discrete events, such as serious crime. It assumes that (1) the underlying process the program wishes to change is a Poisson process in which events occur at a constant average rate per unit time, (2) the evaluation's purpose is to estimate change in the Poisson rate produced by the program, (3) evaluation resources are constrained, and (4) the evaluator has some prior estimates of these rates. The paper first addresses dividing limited evaluation resources between baseline and experimental phases of fixed duration. It then contrasts this optimal fixed design with a simpler approach that allocates half the resources to each phase of the evaluation. The authors then explain their optimal flexible design where the decision to terminate the baseline is not made before the evaluation begins. They give an algorithm for computing rules to tell the evaluator whether to switch after observing a given count of events over a given number of baseline days. Examples demonstrate that it is possible to make notably better estimates of the change in Poisson rate by reacting to baseline data as they appear. Reductions in mean square error of 30 percent were common in the cases examined. The paper also shows that the use of accurate and strongly held priors leads to better estimates than would be achieved in an equal allocation design. Formula and graphs are provided. (Author abstract modified)