At the end of the dose escalation stage of Phase I trials, investigators occasionally enroll additional patients at the maximum tolerated dose (MTD) to further explore the tolerability of the regimen. There is no explicit statistical justification for doing so; neither are there any guidelines regarding the use of toxicity information from this additional cohort with respect to the modification of MTD if necessary. This article addresses both of these issues using a Bayesian approach to model the probability of dose limiting toxicity (DLT) at the MTD. This approach takes the sequential nature of the Phase I design into account and provides predictive and posterior distributions through which various probabilities of interest can be calculated. The results suggest that MTD is usually not well defined with a cohort of 3-6 patients in the traditional dose escalation schema. Therefore, enrolling additional patients at the MTD is recommended. Also demonstrated are different ways to use the posterior density, after the additional cohort is enrolled, to decide whether the MTD is unacceptably toxic.