When optimal monetary policy is subject to a credibility problem, it is often argued that the government should appoint a central banker whose incentives differ from the government's. I argue, however, that such delegation does not overcome credibility problems given that delegation is discretionary and without costs. "Reappointment costs" of delegation are shown to improve suboptimal outcomes, but credibility of optimal monetary policy turns out to be worsened. At best, delegation therefore has no effects on credibility, but only if reappointment has no costs.