We model the preferences of a decision-maker by means of two binary relations. The first of these is transitive and captures comparisons that the agent finds easy or obvious. The second one describes the choices of the agent from binary choice problems, and it is assumed to be complete. Imposing two consistency conditions on these relations yields what we call a preference structure. The primary goal of the paper is to study the choice behavior that arises from preference structures. We show that the choice theory developed here, while much more general, embodies existence and uniqueness properties that parallel those of the classical choice theory. It also retains considerable predictive power.