The continual reassessment method as described by O'Quigley, Pepe, and Fisher (1990, Biometrics 46, 33-48) leans to a large extent upon a Bayesian methodology. Initial experimentation and sequential updating are carried out in a natural way within the context of a Bayesian framework. In this paper we argue that such a framework is easily changed to a more classic one leaning upon likelihood theory. The essential features of the continual reassessment method remain unchanged. In particular, large sample properties are the same unless the prior is degenerate. For small samples and as far as the final recommended dose level is concerned, simulations indicate that there is not much to choose between a likelihood approach and a Bayesian one. However, for in-trial allocation of dose levels to patients, there are some differences and these are discussed. In contrast to the Bayesian approach, a likelihood one requires some extra effort to get off the ground. This is because the likelihood equation has no solution until we observe a toxicity. Initially then we suggest working with either a standard Up-and-Down scheme or standard continual reassessment method until toxicity is observed and then switching to the new scheme.