A dynamic general equilibrium model of a small open economy is presented where agents may choose the frequency of price changes. A fixed exchange rate is compared to inflation targeting and money targeting. A fixed rate generates more price flexibility than the other regimes when the expenditure switching effect is relatively weak, while money targeting generates more flexibility when the expenditure switching effect is strong. These endogenous changes in price flexibility can lead to changes in the welfare performance of regimes. But, for the model calibration considered here, the extra price flexibility generated by a peg does not compensate for the loss of monetary independence. Inflation targeting yields the highest welfare level despite generating the least price flexibility of the three regimes considered.