An adaptive procedure for sequential clinical trials is considered, in which an increasing proportion of patients is assigned to the better of two treatments as evidence for it accumulates. The procedure considered is a multi-stage application of an optimum two-stage procedure. In the first stage of the two-stage procedure patients are assigned to each of two treatments and in the second all are assigned to the apparently better of the two treatments. The optimum two-stage procedure is one in which the proportions assigned to each of the treatments in the first stage, 2pθ and 2p(1 — θ), are such as to minimize a certain natural cost function, which depends on information available before the first stage and on the total number of patients to be treated. Multi-Stage application consists of recalculating the optimum two-stage θ at each point in the sequential stream of patients and interpreting it as the proportion of the next “small” batch of patients to be assigned to treatment 1. This multi-stage procedure is not optimum but does lead to lower costs than the optimum two-stage procedure.