The problem of point and interval estimation following a Phase I trial, carried out according to the scheme outlined by O'Quigley, Pepe, and Fisher (1990, Biometrics 46, 33-48), is investigated. A reparametrization of the model suggested in this earlier work can be seen to be advantageous in some circumstances. Maximum likelihood estimators, Bayesian estimators, and one-step estimators are considered. The continual reassessment method imposes restrictions on the sample space such that it is not possible for confidence intervals to achieve exact coverage properties, however large a sample is taken. Nonetheless, our simulations, based on a small finite sample of 20, not atypical in studies of this type, indicate that the calculated intervals are useful in most practical cases and achieve coverage very close to nominal levels in a very wide range of situations. The relative merits of the different estimators and their associated confidence intervals, viewed from a frequentist perspective, are discussed.