A dose–schedule-finding trial is a new type of oncology trial in which investigators aim to find a combination of dose and treatment schedule that has a large probability of efficacy yet a relatively small probability of toxicity. We demonstrate that a major difference between traditional dose-finding and dose–schedule-finding trials is that while the toxicity probabilities follow a simple nondecreasing order in dose-finding trials, those of dose–schedule-finding trials may adhere to a matrix order. We show that the success of a dose–schedule-finding method requires careful statistical modeling and a sensible dose–schedule allocation scheme. We propose a Bayesian hierarchical model that jointly models the unordered probabilities of toxicity and efficacy and apply a Bayesian isotonic transformation to the posterior samples of the toxicity probabilities, so that the transformed posterior samples adhere to the matrix-order constraints. On the basis of the joint posterior distribution of the order-constrained toxicity probabilities and the unordered efficacy probabilities, we develop a dose–schedule-finding algorithm that sequentially allocates patients to the best dose–schedule combination under certain criteria. We illustrate our methodology through its application to a clinical trial in leukemia and compare it with two alternative approaches. Copyright © 2008 John Wiley & Sons, Ltd.