Phase I cancer chemotherapy trials are designed to determine rapidly the maximum tolerated dose of a new agent for further study. A recently proposed Bayesian method, the continual reassessment method, has been suggested to offer an improvement over the standard design of such trials. We find the previous comparisons did not completely address the relative performance of the designs as they would be used in practice. Our results indicate that with the continual reassessment method, more patients will be treated at very high doses and the trials will take longer to complete. We offer some suggested improvements to both the standard design and the Bayesian method.