The paper proposes an optimal response-adaptive procedure for a general class of responses using a combination of two clinically relevant optimality criteria. We provide a thorough development for trials involving two treatments and sketch the possible extension for multiple treatments. Some related asymptotic results are worked out. We provide simulation studies to compare the performance of the proposed procedure with some of the existing competitors. We illustrate our methodology on data from a real clinical trial. © 2009 VVS.