Clinical trials in which both efficacy (E) and toxicity (T) are used to choose doses adaptively for successive cohorts of patients based on the accumulating dose-outcome data are commonly called “phase I-II” trials. We describe a Bayesian method1, 2 for the design and conduct of such trials that utilizes two types of decision criteria, each defined in terms of the probabilities π_E(x, θ) and π_T(x, θ) of E and T for a patient given dose x, where θ denotes the model parameter vector. The first criterion consists of a fixed lower limit on π_E(x, θ) and a fixed upper limit on π_T(x, θ), which are used together to determine whether x is acceptable. The second criterion is a set of elicited target probability pairs π = (π_E,π_T) that embody equally desirable trade-offs between E and T. These elicited target trade-offs pairs are used to construct a function giving the distance between a given (π_E,π_T) pair and the ideal point (1, 0) corresponding to certain efficacy without toxicity. Pairs closer to the ideal are more desirable. The function is constructed so that the elicited pairs are equally distant from the ideal. Each time a dose must be chosen based on the current interim data, , the desirability of each acceptable dose x is defined to be the desirability of the contour containing the pair of posterior means . The next cohort is then given the most desirable dose, and this criterion also is used to select a best dose at the end of the trial.