This paper challenges the logical consistency of the Barro and Gordon (1983) type of model of policy credibility, in which agents have 'trigger strategy' expectations of policy. It is shown that optimal policy is to 'cheat' by announcing low inflation whilst pursuing high inflation. This implies that the trigger mechanism is incompatible with rational expectations and there are no equilibria that simultaneously satisfy all the model assumptions. Finally, following a review of rational expectations models, it is suggested that policy credibility can be adequately described by a model in which expectations are adaptive, without regard for whether they are also rational.