In phase I clinical trials, experimental drugs are administered to healthy volunteers in order to establish their safety and to explore the relationship between the dose taken and the concentration found in plasma. Each volunteer receives a series of increasing single doses. In this paper a Bayesian decision procedure is developed for choosing the doses to give in the next round of the study, taking into account both prior information and the responses observed so far. The procedure seeks the optimal doses for learning about the dose–concentration relationship, subject to a constraint which reduces the risk of administering dangerously high doses. Individual volunteers receive more than one dose, and the pharmacokinetic responses observed are, after logarithmic transformation, treated as approximately normally distributed. Thus data analysis can be achieved by fitting linear mixed models. By expressing prior information as ‘pseudo-data’, and by maximizing over posterior distributions rather than taking expectations, a procedure which can be implemented using standard mixed model software is derived. Comparisons are made with existing approaches to the conduct of these studies, and the new method is illustrated using real and simulated data.