In a dynamic New Keynesian optimizing model, we introduce incomplete exchange rate pass-through on import prices. Three results stand out. First, unlike canonical models with perfect pass-through which emphasize a type of isomorphism, incomplete pass-through renders the analysis of monetary policy of an open economy fundamentally different from the one of a closed economy. Second, productivity-driven deviations from the law of one price assume the interpretation of endogenous cost-push shocks. Third, the optimal commitment policy, relative to discretion, entails a smoothing of the deviations from the law of one price and requires more stable nominal and real exchange rates.