Using genetic programming, we find trading rules that generate significant excess returns for three of four EMS exchange rates over the out-of-sample period 1986- 1996. Permitting the rules to use information about the interest rate differential proved to be important. The reduction in volatility resulting from the imposition of a narrower band may reduce trading rule profitability. Our results cannot be duplicated by commonly used moving average rules, filter rules or by two rules designed to exploit known features of target zone rates. There is no evidence that the excess returns are compensation for bearing systematic risk.