Many empirical studies have shown that preferences are reference-dependent, implying loss aversion. Because reference-dependence is a relatively new concept, there exists little theory on it. The theories that are available generally take the reference point as given and then impose the traditional assumptions such as completeness of preferences. Reference-dependence raises, however, new problems that do not occur in reference-independent theories. This paper argues that in the empirically realistic case where the reference point is always an element of the decision maker’s opportunity set, reference-dependent preferences are, according to the principles of revealed preference, necessarily incomplete. A new model of decision under uncertainty is presented that extends prospect theory to cover this case. The paper also gives preference foundations for two special cases: one in which utility is decomposed into a normative and a psychological component and one in which loss aversion is constant. The latter case has frequently been used in empirical research and in applied decision analysis.