When the population size of an aggregate unit is small relative to the offense rate, crime rates must be computed from a small number of offenses. Such data are ill-suited to least-squares analysis. Poisson-based regression models of counts of offenses are preferable because they rest on assumptions about error distributions that are consistent with the nature of event counts. A simple elaboration transforms the Poisson model of offense counts to a model of offense rates per capita. Using this method to analyze juvenile arrest rates for robbery in 264 nonmetropolitan counties in 4 States revealed the method’s advantages. The negative binomial variant of Poisson regression effectively resolved difficulties that arise in ordinary least-squares analyses. Figures, tables, and 18 references (Author abstract modified)