Phase II trials often test the null hypothesis H0: p≤p0 versus H1: p≥p1 , where p is the true unknown proportion responding to the new treatment, p0 is the greatest response proportion which is deemed clinically ineffective, and p1 is the smallest response proportion which is deemed clinically effective. In order to expose the fewest number of patients to an ineffective therapy, phase II clinical trials should terminate early when the trial fails to produce sufficient evidence of therapeutic activity (i.e. if p≤p0). Simultaneously, if a treatment is highly effective (i.e. if p≥p1), the trial should declare the drug effective in the fewest patients possible to allow for advancement to a phase III comparative trial. Several statistical designs, including Simon's minimax and optimal designs, have been developed that meet these requirements. In this paper, we propose three alternative designs that rely upon stochastic curtailment based on conditional power. We compare and contrast the properties of the three approaches: (1) stochastically curtailed (SC) binomial tests, (2) stochastically curtailed (SC) Simon's optimal design, and (3) SC Simon's minimax design to those of Simon's minimax and Simon's optimal designs. For each of these designs we compare and contrast the number of opportunities for study termination, the expected sample size of the trial under the null hypothesis (p≤p0), and the effective type I and type II errors. We also present graphical tools for monitoring phase II clinical trials with stochastic curtailment using conditional power. Copyright © 2006 John Wiley & Sons, Ltd.