As with most analyses involving microdata, applications of count data models must somehow account for unobserved heterogeneity. The count model literature has generally assumed that unobservables and observed covariates are statistically independent. Yet for many applications this independence assumption is clearly tenuous. When the unobservables are omitted variables correlated with included regressors, standard estimation methods will generally be inconsistent. Though alternative consistent estimators may exist in special circumstances, it is suggested here that a nonlinear instrumental-variable strategy offers a reasonably general solution to such estimation problems. This approach is applied in two examples that focus on cigarette smoking behavior.