Policy-makers often justify their choice of fixed exchange rate regimes as a shelter against nonfundamental influences in the foreign exchange market. This paper proposes a framework, based on endogenous noise trading, which makes sense of the policy-makers' view. We show that as a result of multiple equilibria, the model violates Mundell's “Incompatible Trinity:” under some conditions, it is possible to reduce the volatility of the exchange rate without any sacrifice in terms of monetary autonomy. We provide empirical evidence supportive of the existence of a nonfundamental channel in the link between exchange rate regimes and exchange rate volatility. If … markets come to believe exchange rate stability is not itself a significant policy objective, we should not be surprised that snowballing cumulative movements can develop that appear widely out of keeping with current balance-of-payments prospects or domestic price movements. At that point, freely floating exchange rates, instead of delivering on the promise of money autonomy for domestic monetary or other policies, can greatly complicate domestic economic management [Paul Volcker 1978–79, p. 9].