The Continual Reassessment Method (CRM) is a Bayesian phase I design whose purpose is to estimate the maximum tolerated dose of a drug that will be used in subsequent phase II and III studies. Its acceptance has been hindered by the greater duration of CRM designs compared to standard methods, as well as by concerns with excessive experimentation at high dosage levels, and with more frequent and severe toxicity. This paper presents the results of a simulation study in which one assigns more than one subject at a time to each dose level, and each dose increase is limited to one level. We show that these modifications address all of the most serious criticisms of the CRM, reducing the duration of the trial by 50-67 per cent, reducing toxicity incidence by 20-35 per cent, and lowering toxicity severity. These are achieved with minimal effects on accuracy. Most important, based on our experience at our institution, such modifications make the CRM acceptable to clinical investigators.