When a country abandons a fixed, or target zone exchange regime it usually claims that the regime was "fundamentally" sound but that it was undermined by pernicious speculation. The validity of the claim is impossible to assess using only observable data-there always exists a future path of current account surpluses that would make the regime sound, and speculators' (investors'?) motives are unobservable. This paper analyzes the crucial role of imperfect credibility in a currency crisis with a stochastic dynamic rational expectations regime switch model. The exchange regime is sound, e.g., a currency board-the only market failure is that the Central Bank cannot make a credible commitment to maintain the regime. The paper has two innovations: (1) It specifies the cost of imperfect credibility, and (2) It quantifies the cost of imperfect credibility. Imperfect credibility generates small (but costly) average interest rate differentials. Imperfect credibility cannot generate large interest differentials, but a surprisingly small "fundamental" currency overvaluation added to the basic specification generates large interest rate differentials. The paper's main result- that a lack of credibility cannot generate large interest rate differentials in a sound regime-is robust. The model in the paper is stylized, but the results are rich. The policy maker (Central Bank) and investors optimize. Investors fear devaluation and the Bank cannot make a credible commitment to allay their fears. Investors demand an agency currency premium. There is no pernicious speculation-the premium fairly prices the country's assets but it increases the country's cost of capital. The Bank abandons the regime when the expected present value of the agency cost of capital outweighs the expected present value of the benefit from remaining in the regime. The model generates multiple rational expectations equilibria and a variety of patterns linking the exchange rate to the interest rate differential. I parameterized the model using estimates of the exchange rate process for Hong Kong. The model generated agency currency premiums average ½%. The model generated interest rate differentials are consistent with the interest differentials in Hong Kong before the Asian financial crisis in July of 1997. After July 1997 a lack of credibility is not sufficient to explain the observed interest rate differentials of 4-6%.