Hurdle models are frequently used to model count data. Recent developments in the count data literature make it possible to relax commonly imposed assumptions of these models. On the basis of these findings, two extensions of hurdle models that make popular specifications more flexible are developed. Both extensions nest the models that have been used so far, so they can be tested by appropriate parametric restrictions. An example from health economics illustrates the relevance of both model extensions. Copyright © 2012 John Wiley & Sons, Ltd.