In phase II cancer trials, tumour response is either the primary or an important secondary endpoint. Tumour response is a binary composite endpoint determined, according to the Response Evaluation Criteria in Solid Tumors, by (1) whether the percentage change in tumour size is greater than a prescribed threshold and (2) (binary) criteria such as whether a patient develops new lesions. Further binary criteria, such as death or serious toxicity, may be added to these criteria. The probability of tumour response (i.e. ‘success' on the composite endpoint) would usually be estimated simply as the proportion of successes among patients. This approach uses the tumour size variable only through a discretised form, namely whether or not it is above the threshold. In this article, we propose a method that also estimates the probability of success but that gains precision by using the information on the undiscretised (i.e. continuous) tumour size variable. This approach can also be used to increase the power to detect a difference between the probabilities of success under two different treatments in a comparative trial. We demonstrate these increases in precision and power using simulated data. We also apply the method to real data from a phase II cancer trial and show that it results in a considerably narrower confidence interval for the probability of tumour response.