A subset selection rule is considered for selecting the best ofkbinomial populations (as determined by the binomial probability parameter). LetXidenote the number of conforming items in a sample of sizenfrom theithpopulation (success probabilitypi),i= 1,…,k.The rule selects theithpopulation if and only if, where d is a nonnegative integer. Operating characteristics are studied for slippage and equi-spaced parametric configurations. Tables and graphs relating to selection probabilities and expected subset size are presented as well as examples for illustrating their use. Also, a new rule is discussed for selecting populations when bounds on the probability parameters are available.