We study the effects on the optimal monetary policy design problem of allowing for deviations from the law of one price in import goods prices. We reach three basic results. First, incomplete pass-through renders the analysis of monetary policy of an open economy fundamentally different from the one of a closed economy, unlike canonical models with perfect pass-through which emphasize a type of isomorphism. Second, and in response to efficient productivity shocks, incomplete pass-through has the effect of generating endogenously a short-run tradeoff between the stabilization of inflation and of the output gap. Third, in studying the optimal program under commitment relative to discretion, we show that the former entails a smoothing of the deviations from the law of one price, in stark contrast with the established empirical evidence. In addition, an optimal commitment policy always requires, relative to discretion, more stable nominal and real exchange rates.