In phase I oncology trials conducted over the past few decades, the maximum tolerated dose (MTD) has usually been estimated by the traditional escalation rule (TER), which traces back to 1973. In the meantime, new methods have been proposed which hope to estimate the true MTD more precisely than the TER while using less patients. In this simulation study, TER is compared with the accelerated titration dose design (ATD), two up-and-down designs (biased coin design, r-in-a-row (RIAR)), the maximum likelihood version of the continual reassessment method (CRML), and a Bayesian method that is implemented in the software Bayesian ADEPT (assisted decision-making in early phase trials). Each design was applied to 50,000 simulated studies. The designs were then compared for accuracy in detecting the true MTD (which is known here), while taking into account the average number of patients and toxicities per run. In terms of accuracy, ADEPT outperformed the other methods in the scenario with medium toxicity and was close to the best methods in the low and high toxic scenarios. The average number of patients needed per run was the lowest for TER in the scenario with low toxicity and for ADEPT in the remaining scenarios. The longer the escalation path to the target region of the MTD, the more the difference in the average number of patients per run pronounced between TER and ADEPT. TER induced least toxicities in all scenarios. ADEPT turned out to be quick and accurate in determining the MTD, while TER was the safest but least accurate method. CRML was as accurate as TER, and the up-and-down designs did not excel. Bayesian ADEPT is considered a valuable tool for the conduct of phase I dose-escalation trials in oncology, but careful preparation is indispensable before its practical use.