Central bank policy suffers from time-inconsistency when facing a banking crisis : A bailout is optimal ex post but ex ante it should be limited to control moral hazard. Dollarization provides a credible commitment not to help at the cost of not helping even when it would be ex ante optimal to do so. Dollarization is good when the costs of establishing a reputation for the central bank are high, monitoring effort by the banker is important in improving returns, and when the cost of liquidating projects is moderate. However, a very severe moral hazard problem could make dollarization Undesirable. The results obtained are applied to assess the desirability of dollarization in a range of countries and the potential role of the IMF as International LOLR.