The increasing emergence of predictive markers for different treatments in the same patient population allows us to define stratified treatment strategies. We consider randomized clinical trials that compare a standard treatment with a new stratified treatment strategy that divides the study population into subgroups receiving different treatments. Because the new strategy may not be beneficial in all subgroups, we consider in this paper an intermediate approach that establishes a treatment effect in a subset of patients built by joining several subgroups. The approach is based on the simple idea of selecting the subset with minimal p-value when testing the subset-specific treatment effects. We present a framework to compare this approach with other approaches to select subsets by introducing three performance measures. The results of a comprehensive simulation study are presented, and the relative merits of the various approaches are discussed. Copyright © 2016 John Wiley & Sons, Ltd.