The main result of Meese and Rogoff [1983 a,b] is that small structural exchange rate models forecast major dollar exchange rates no better than a naive random walk model. This result obtains even when the model forecasts are based on actual realized values of the explanatory variables. Here we improve our methodology by implementing a new test of out-of-sample fit; the test is valid even for overlapping long-horizon forecasts. We find that the dollar exchange rate models perform somewhat less badly over the recent Reagan regime period than over the episodes studied previously. The methodology is also applied to the mark/yen and mark/pound exchange rates, and to real exchange rates. Finally, we test to see if real exchange rates and real interest differentials can be represented as a cointegrated process. The evidence suggests that there is no single common influence inducing nonstationarity in both real exchange rates and real interest differentials.