Several problems in economic theory can be formulated as a dynamic programming problem, plus an additionalincentive compatibilityconstraint. This constraint requires the continuation value along the chosen sequence, at any point in time, to be larger than some prescribed function of the state, the control, or perhaps both. This constraint changes the nature of the problem in a substantial way: for instance, even if the problem is discounted, standard arguments based on contraction principles do not apply. In this paper we show how to reduce this class of problems to a simple variation of standard dynamic programming techniques. In particular the value function for the problem is shown to be the fixed point of an appropriately defined operator.Journal of Economic LiteratureClassification Numbers: C61, C72, C73, D92.