Should central banks’ inflation targets remain set in stone? We study a dynamic mechanism design problem between a government (principal) and a central bank (agent). The central bank has persistent private information about structural shocks. Firms learn the state from the central bank’s reports and form inflation expectations. A dynamic inflation target implements the full-information commitment allocation. The central bank is delegated the authority to adjust the level and flexibility of its target as long as it does so one period in advance. All history dependence of the mechanism is summarized by the current period’s target. We show that a declining natural interest rate and a flattening Phillips curve imply opposite optimal target adjustments. We leverage our framework to study longer-horizon time consistency problems and speak to practical policy questions of inflation target design.