This paper addresses an interesting theoretical intuition, originally put forward in De Grauwe (1989), according to which market efficiency should find stronger support in a pegged exchange rate regime rather than in a purely floating context. A cointegration-based empirical investigation on the French Franc/Deutsche Mark exchange rate and two outstanding floating rates (DM/U$, Yen/U$) strongly supports the above intuition. As revealed by cointegration tests, a necessary condition for market efficiency is uniformly supported across alternative exchange rate regimes. Forward unbiasedness tests, however, point out that only inside the EMS is a sufficient condition for foreign exchange market efficiency satisfied. The above conclusion is robust to alternative methodologies to test restrictions on parameters and has relevant implications on a large strand of applied literature assessing EMS credibility.