Phase II study designs are proposed that evaluate both clinical response and toxicity, and that are similar in structure to Simon's two-stage designs. Sample sizes and decision criteria are chosen to minimize the maximum expected accrual, given that the treatment is unacceptable either in terms of clinical response or toxicity. This is achieved subject to control of error rates, either uniformly over all possible correlation structures linking response and toxicity, or alternatively, under an assumption of independence between response and toxicity. In the latter case, bounds on the error rates show that effective control is still uniformly achieved even if the independence assumption is relaxed.