CPI inflation targeting necessitates a flexible exchange rate regime. This paper embeds an endogenous target rule into a simple open economy macro model to explain the UIP puzzle. The model predicts that the change in the exchange rate is inversely related to the lagged interest rate differential. Openness and aversion to inflation variability determine the strength of this linkage. Foreign inflation and the foreign interest rate also affect exchange rate changes. This hypothesis is tested on data from three small open economies, Canada, Norway, and Switzerland, all of which target CPI inflation and maintain extensive trade and finance links with a larger neighboring country. Supportive evidence is strongest for Switzerland during a clean float period before the outbreak of the Global Financial Crisis.