Bechhofer and Kulkarni (1982) proposed procedures for selecting that one ofkBernoulli populations with the largest single trial success probability. They showed that their procedure fork= 2 minimizes the expected total sample size amongst a class of procedures, all of which attain the same probability of correct selection. Kulkarni and Jennison (1986) generalized this result to the casek≥ 3. In this article we prove the stronger result that the Bechhofer-Kulkarni procedure for eachk≥2 stochastically minimizes the distribution of sample size amongst procedures in the same class. That is, the distribution of sample size for the Bechhofer-Kulkarni procedure is the same as or stochastically smaller than that for any other procedure in the class.