Abstract In this article the Colton fixed sample size model for choosing the better of two treatments is extended by including those patients who did not participate in the experiment prior to deciding which treatment is superior. The optimum Bayesian solutions are found for normal observations and comparisons are made between them and the corresponding results based on Colton's model. Considerably different results are generally obtained by the proposed model as compared to Colton's model in terms of both sample size and risk.