The continual reassessment method (CRM) is a method for estimating the maximum tolerated dose in a dose-finding study. Traditionally, use is made of a single working model or ‘skeleton’ idealizing an underlying true dose–toxicity relationship. This working model is chosen either by discussion with investigators or published data, before the beginning of the trial or simply on the basis of operating characteristics. To overcome the arbitrariness of the choice of such a single working model, Yin and Yuan (biJ. Am. Statist. Assoc. 2009; 104:954–968) propose a model averaging over a set of working models. Here, instead of averaging, we investigate some alternative Bayesian model criteria that maximize the posterior distribution. We propose three adaptive model-selecting CRMs using the Bayesian model selection criteria, in which we specify in advance a collection of candidate working models for the dose–toxicity relationship, especially initial guesses of toxicity probabilities, and adaptively select the only one working model among the candidates updated by using the original CRM for each working model, based on the posterior model probability, the posterior predictive loss or the deviance information criteria, during the course of the trial. These approaches were compared via a simulation study with the model averaging approach. Copyright © 2011 John Wiley & Sons, Ltd.