It is shown that a test suggested by Bechhofer, Kiefer, and Sobel [1], for selecting the better of two binomial populations, can be formulated and solved when a maximum number of tests is specified. It is assumed that the probability of correctly selecting the better population is specified to be better than P* when the difference in success probabilities exceeds a specified Δ*. The populations are sampled equally and it is assumed that the trial ends either when the difference in the number of successes exceeds a calculated value of s, or when N tests have been made, whichever is sooner.