One of the most important aspects of a phase I trial or other acute toxicity study is estimating accurately the probability of toxicity that is associated with the recommended dose. We use the biased coin up-and-down design to allocate and isotonic regression to estimate toxicity probabilities and determine the recommended dose. We then derive, using bootstrap methods, an estimate of the probability of toxicity at the recommended dose. Small sample properties of this estimator are also evaluated. Published in 2003 by John Wiley & Sons, Ltd.