The problem of selecting thet“best” populations from a set ofkpopulations is considered where the observations (possibly already condensed) are of independent random variablesYi, fori= 1, …,k, with distribution functionsF(y; θi), which are nonincreasing in the θifor ally. The selection process is based on the values of theY1, …,Yk(ties being broken by randomization), and a theorem is proved which enables us to decide on a “least favorable configuration” for the θivalues.