Asbtract:  The simplest way to model count data with extra zeros seems to be to include an extra spike at the origin, forming effectively a mixture distribution with a degenerate component. Nonetheless, there are at least two different ways of forming the mixture. It seems not to be widely appreciated that, at least when covariates are included, two different models result. In this talk we will describe the two models, make a detailed comparison of them and discuss the implications for data analysis.