We formulate a stochastic rational-expectations model of exchange rate determination in which there are random shocks to the process of sluggish price adjustment. We examine the effects of imposing limits upon the range of variation of both nominal and real exchange rates, and describe the intervention policies needed to defend the bands in each case. We consider the possibility that commitment to defend a particular nominal band may be less than fully credible, and analyze the implications of operating certain rules for realignment. We contrast our results with those which arise in the Krugman model of a nominal band.