This paper presents an exact method for the analysis of a phase II cancer clinical trial conducted using a two-stage design in which early stopping may be allowed for either futility or efficacy. The method provides a point and interval estimate of the response probability associated with the treatment under investigation and a p-value for testing whether this exceeds some standard null value. Two-stage designs are often used in phase II trials in oncology for reasons of ethics and efficiency, but this design feature is seldom taken into account when the results are analyzed. After any two-stage design or multi-stage design, the method for analysis should take into account the previous interim analyses performed, otherwise the results will be biased. In this paper, an approximate approach based on a log-odds ratio parameterisation will be compared with an exact method through the calculation of the precise coverage probabilities of each approach. Copyright © 2010 John Wiley & Sons, Ltd.