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How should policy be optimally designed when a monetary authority faces a private sector that is somewhat skeptical about policy announcements and which interprets economic data as providing evidence about the monetary authorityís preferences or its ability to carry through on policy plans? To provide an answer to this question, we extend the standard New Keynesian macroeconomic model to include imperfect ináation control (impementation error relative to an ináation action) and Bayesian learning by private agents about whether the monetary authority is the committed type (capable of following through on announced plans) or an alternative type (producing higher and more volatile ináation). In a benchmark case, we Önd that optimal policy involves dramatic anti-ináation actions which include an interval of deáation during the early stages of a plan, motivated by investing in a reputation for strength. Such policies resemble recommendations during the 1980s for a "cold turkey" approach to disináation. However, we also Önd that such policy is not robustly optimal. A more "gradualist" policy arises if the initial level of credibility is very low. We also investigate a setting where the alternative monetary authority follows a simple behavioral rule that mimics variations in the committed authorityís policy action but with a bias toward higher and more volatile ináation. In this case, which we call a "tag along" alternative policymaker, a form of gradualism is always optimal.