Decades of research in decision making have established thatthere are some situations where human judgments cannot bemodelled according to classical probability theory. Yet if weabandon classical (Bayesian) probability theory as an overar-ching framework for constructing cognitive models, what dowe replace it with? In this contribution we outline a way to di-vide the space of possible computational level models of prob-abilistic judgment into a hierarchy of levels of increasing com-plexity, with classical Bayesian probability models occupyingthe lowest level. Each level has a unique experimental sig-nature, and we examine which level is best able to describehuman behavior in a particular probabilistic reasoning task.