In a typical two-stage design employed in a phase II cancer clinical trial for efficacy screening, a fixed number of patients are initially enrolled. The trial may be terminated for lack of clinical efficacy of treatment if the observed number of treatment successes after the first stage is too small. Otherwise, an additional fixed number of patients are enrolled to accumulate additional information on efficacy. Simon's optimal design and minimax design have often been applied to designing phase II clinical trials. Other designs have largely been ignored. In this paper, we introduce a graphical method to search for a good design that is a compromise between the optimal and the minimax designs.