The most common primary statistical end point of a phase II clinical trial is the categorization of a patient as either a ‘responder’ or ‘nonresponder’. The primary objective of typical randomized phase II anticancer clinical trials is to evaluate experimental treatments that potentially will increase response rate over a historical baseline and select one to consider for further study. We propose single-stage and two-stage designs for randomized phase II clinical trials, precisely defining various type I error rates and powers to achieve this objective. We develop a program to compute these error rates and powers exactly, and we provide many design examples to satisfy pre-fixed requirements on error rates and powers. Finally, we apply our method to a randomized phase II trial in patients with relapsed non-Hodgkin's disease. Copyright © 2013 John Wiley & Sons, Ltd.