In this article we consider how revealed preference inferences change when the assumptions maintained are altered. In the first two models, a demand correspondence is generated by utility maximization; the conditions on the underlying preference relation differ only with respect to the strength of the convexity assumptions. In the second two models, alternative revealed preference axioms are imposed directly on a demand correspondence. One of these axioms is Samuelson's Weak Axiom of Revealed Preference; the other is a variant of this axiom which allows for nonuniqueness in the demand correspondence. The results of our analysis clarify aspects of the existing revealed preference literature.