Previous research has suggested that including exchange rate stabilisation within the goals of monetary policy significantly increases the volatility of inflation, output and interest rates, and that the benefits of exchange rate stabilisation therefore do not justify the costs. The current paper tests whether this finding is robust when various alternative models of exchange rate determination are considered. The analysis is carried out in the context of optimal full-information monetary policy rules in a New Keynesian model that is calibrated to represent the New Zealand economy. For the models that feature rational expectations, we support the conclusion that seeking to avoid exchange rate volatility would have more costs than benefits. Indeed, a major cost of including the exchange rate within the goals of monetary policy is that inflation expectations become less anchored to the inflation target, meaning that larger movements in nominal interest rates are required to control inflation.