Many new experimental treatments benefit only a subset of the population. Identifying the baseline covariate profiles of patients who benefit from such a treatment, rather than determining whether or not the treatment has a population-level effect, can substantially lessen the risk in undertaking a clinical trial and expose fewer patients to treatments that do not benefit them. The standard analyses for identifying patient subgroups that benefit from an experimental treat- ment either make separate marginal inferences on each individual, which raises multiplicity issues, or focus inappropriately on the presence or absence of treatment-covariate interactions. We propose a Bayesian ”credible subgroups” method to identify two bounding subgroups for the benefiting sub- group: one for which it is likely that all members simultaneously have a treatment effect exceeding a specified threshold, and another for which it is likely that no members do. We examine frequentist properties of our method via simulation, and illustrate the approach using data from an Alzheimer’s disease treatment trial. Time permitting, we will also discuss recent extensions to the case of multiple treatments and multiple trial endpoints (in our dataset, two for efficacy and one for safety).