Using a general method for obtaining confidence intervals from samples from discrete distributions, this article introduces a new confidence interval method for estimating the difference of two binomial probabilities and compares it to three other confidence interval methods, one of which is the usual method with no continuity correction. Each of the other two confidence interval methods uses its own continuity correction; one combines it with an estimate of the standard error that is slightly different from that commonly used. Some values of the “exact” confidence interval limits are also derived. The four confidence interval methods, each of which is based on the normal approximation and can be carried out easily on a hand calculator, are compared in terms of their precision, the agreement of their coverage probabilities with nominal confidence level values, and the smallness of their sample sizes before the normal approximation can be considered appropriate. Coverage probabilities and measures of precision are computed exactly rather than estimated by simulation. On the basis of these comparisons, the new confidence interval method is recommended.