The previous chapter identified various sources of misspecification. This chapter introduces alternative count data models that overcome the restrictiveness of the Poisson specification. Most of these models can be classified according to the particular problem they address as models for unobserved heterogeneity or as models for selectivity, where unobserved heterogeneity reflects a lack of observability of independent variables, whereas selectivity reflects limits in the observability of the dependent variable. Hybrid models exists as well. A third category of models addresses the issue of endogeneity.