This paper studies the cost of limited commitment when a central bank has the discretion to adjust policy whenever the costs of honoring its past commitments become high. Specifically, we consider a central bank that seeks to implement optimal policy in a New Keynesian model by committing to a price-level target path. However, the central bank retains the flexibility to reset the target path if the cost of adhering to it exceeds a social tolerance threshold. We find that endowing the central bank with such discretion undermines the credibility of the price-level target and weakens its effectiveness to stabilize the economy through expectations. The endogenous nature of credibility also brings novel results relative to models with exogenous timing of target resets. A much higher degree of credibility is needed to realize the stabilization benefits of commitment. Multiple equilibria also emerge, including a low credibility equilibrium with frequent target resets and high volatility.