In this paper an approach is developed that accommodates heterogeneity in Poisson regression models for count data. The model developed assumes that heterogeneity arises from a distribution of both the intercept and the coefficients of the explanatory variables. We assume that the mixing distribution is discrete, resulting in a finite mixture model formulation. An EM algorithm for estimation is described, and the algorithm is applied to data on customer purchases of books offered through direct mail. Our model is compared empirically to a number of other approaches that deal with heterogeneity in Poisson regression models.