Under a large degree of extrinsic inflation persistence, there is a strong yet simple case for inflation targeting even if we are uncertain about many other dimensions of the economy. If inflation persistence is high and driven by extrinsic sources, even an excessively strict inflation-targeting regime is preferable to full policy discretion. Our result is entirely built on stabilization policy: long-run inflation rates are optimal under full policy discretion in our model. It is instead the medium-term dynamics of inflation expectations that render the policy response under discretion worse than inaction.