Phase I clinical trials of cancer chemotherapy drugs are intended to determine the maximum tolerable dose (MTD). Thestandard method employed is a rule-based dose-escalation scheme in which escalation depends on the number of patients at a dose level that have dose-limiting toxicity (DLT). The MTD is thus defined in terms of the rules and a series of dose levels selected for sampling. For some trials it is desirable to have a more precise definition of the MTD, and to determine the MTD more accurately than possible with the rule-based schemes. Continuous reassessment methods (CRMs) define the MTD to be the dose at which a fixed fraction of patients experience DLT, and thus appear suited to these trials. It is shown, however, that these methods can have failure modes that in fact make them unattractive. An alternative data-driven dose-finding method is described that combines the robustness of the rule-based methods and with features of CRMs. The method has two stages. In the first stage, doses are escalated by a factor of 1.5. In the second stage, which begins at the first instance of DLT, a two-parameter logistic dose-response model estimates the MTD from the DLT experience of all patients. The model is initialized by setting the dose (d10) at which 10 per cent of patients would experience DLT to half the dose at which the first DLT was observed, and the dose (d90) at which 90 per cent would experience DLT to ten times d10. Weights are assigned such that the information at d10 and d90 is equivalent to that of one patient at each of the two doses. Cohorts of three patients are treated in both stages, and the dose for a new cohort in the second stage is the estimated MTD. The only prior information required to specify the design completely is the dose which will be given to the first cohort. Two stopping rules are investigated; among the requirements for these are that at least three (or four) DLTs be observed and at least nine patients be treated in the second stage. Simulations show that a coefficient of variation of approximately 0.4 on a target DLT probability of 0.3 is obtained over a wide variation in dose-response characteristics of the study drug. The performance of the new method is compared to that of rule-based methods.