Several methods have been proposed to construct confidence intervals for the binomial parameter. Some recent papers introduced the ‘mean coverage’ criterion to evaluate the performance of confidence intervals and suggested that exact methods, because of their conservatism, are less useful than asymptotic ones. In these studies, however, exact intervals were always represented by the Clopper–Pearson interval (C–P). Now we focus on Sterne's interval, which is also exact and known to be better than the C–P in the two-sided case. Introducing a computer intensive level-adjustment procedure which allows constructing intervals that are exact in terms of mean coverage, we demonstrate that Sterne's interval performs better than the best asymptotic intervals, even in the mean coverage context. Level adjustment improves the C–P as well, which, with an appropriate level adjustment, becomes equivalent to the mid-P interval. Finally we show that the asymptotic behaviour of the mid-P method is far poorer than is generally expected. Copyright © 2003 John Wiley & Sons, Ltd.