Empirical scientists often are faced with incomplete data and desire imputations for their missing data values. The expectation–maximization algorithm is a generic tool that offers maximum likelihood solutions for such data sets. This article pursues this type of solution for Poisson random variables, utilizing a generalized linear model extension that mirrors the linear analysis of a covariance regression specification. This formulation allows a mixed model to be implemented and contrasted with a Poisson-gamma mixture (i.e., negative binomial) model. Simple comparisons are made between model specification results for a population counts example, with and without a constraint on the total of the missing counts.