Ethical considerations in a cancer phase I trial require a design allowing determination of the maximum tolerated dose with a minimum number of patients treated at low ineffectual or high overly toxic doses. It would also be advantageous to complete the phase I trial in as short a period of time and with as few patients as possible to allow further resources for later studies in which patients are treated at the optimal dose. Several dose escalation schemes are compared. These are the Fibonacci, two two-stage schemes, and a proposed scheme which uses knowledge of all toxicity grades. Estimates of the maximum tolerated dose are obtained and compared using the dose escalation schemes alone, a logit model, and a proposed mean response model. Confidence intervals using the delta method are obtained from the logit and mean response models. The proposed scheme and the two-stage schemes have the advantage of requiring fewer patients, particularly at low doses. Confidence intervals obtained from the mean response model have better coverage than those from the logit model. Data from a cancer phase I trial of dipyridamole and acivicin is presented to illustrate the methods.