Confidence intervals, in general, have become an important aspect of reporting statistical results. In particular, interval estimators for binomial proportions have been studied extensively in recent literature. The large-sample Wald intervals are known to perform poorly, but the Wilson intervals have been shown to perform well in a variety of situations. One criticism is the relative difficulty of computing the Wilson or quadratic intervals in comparison to the Wald intervals. We offer a computational formula for the Wilson intervals that is a weighted estimator of the observed proportion, p, and that based on an uninformative prior, 1⁄2. This contribution enhances our understanding of the coverage behavior of the Wilson intervals. In addition, we contrast the Wilson intervals with other well-known intervals for the case of zero successes. © 2006 Edward Arnold (Publishers) Ltd.