Phase I clinical trials are designed to identify an appropriate dose for experimentation in phase II and III studies. I present the results from a simulation study to evaluate the performance of nine phase I designs involving the standard design, the two-stage modified Storer's design, the two-stage Korn's design, the one-stage modified continual reassessment method (CRM) designs, and the two-stage modified CRM designs. I compare the performance of the above phase I designs in terms of the following criteria: (i) the proportion of the recommended maximum tolerated dose (MTD) at each dose level; (ii) the proportion of patients treated at each dose level; (iii) the average number of patients to complete the trial; (iv) the probability of toxicity observed; and (v) the average number of cohorts to complete the trial. In general, the one-stage modified CRM II and CRM III designs perform well compared with the other designs considered in this study. The one-stage modified CRM II and III designs require much fewer numbers of cohorts than do the two-stage modified CRM II and III designs. The one-stage modified CRM II and III designs avoid the criticisms of the original CRM by reducing the average number of cohorts and toxicity incidences, while estimating the MTD more accurately than does the standard design.