The extent to which exchange rate management can coexist with an independent monetary policy is examined in the context of a model with exchange rate bands. Using a Dornbusch model in which stochastic stocks are added to the Phillips curve, we analyse the implications of assuming that the monetary authorities follow certain simple rules for realigning the band when fundamentals have drifted too far from equilibrium. Assuming that information about whether the band is to be defended or there is to be a realignment is revealed at the point when the exchange rate hits the edge of the band, we show how the path of the exchange rate can be completely characterised in terms of solution to a second order non linear differential equation -- together with jumps in the rate at the edge of the band, which satisfy a zero-profit arbitrage condition. When the realignment is expected with certainty, hysteresis is introduced into the behaviour of the exchange rate