The paper argues that the reason real world fixed exchange rate regime
s usually have finite bands, instead of completely fixed exchange rate
s between realignments, is that exchange rate bands, counter to the te
xtbook result, give central banks some monetary independence, even wit
h free international capital mobility. The nature and amount of moneta
ry independence is specified, informally and in a formal model, and qu
antified with Swedish krona data. Altogether the amount of monetary in
dependence appears sizable. For instance, an increase in the Swedish k
rona band from zero to about +/- 2 percent may reduce the krona intere
st rate's standard deviation by about a half.