In a small open economy with fixed exchange rates, tandard theory suggests that domestic inflation and interest rates should equal those abroad. In a credible target zone, the same theories suggest that inflation and interest rates should be 'close'. Here, we seek to make precise this idea of limits on inflation and interest rate differentials consistent with limits on exchange rate movements. We then examine the case of Ireland, which joined the Exchange Rate Mechanism (ERM) of the European Monetary System (EMS) in 1979 attracted by the prospects of lower, German influenced, inflation and interest rates. We find in the early years of the ERM, both Irish inflation and interest rastes were inconsistent with credibility of the exchange rate regime; in he latter years, from 1987 on, rates were in the derived range around German rates.