A claim of superiority of one intervention over another often depends naturally on results from several outcomes of interest. For such studies the common practice of making conclusions about individual outcomes in isolation can be problematic. For example, an intervention might be shown to improve one outcome (e.g., pain score) but worsen another (e.g., opioid consumption), making interpretation difficult. We thus advocate joint hypothesis testing, in which the decision rule used to claim success of an intervention over its comparator with regard to the multiple outcomes are specified a priori, and the overall type I error is protected. Success might be claimed only if there is a significant improvement detected in all primary outcomes, or alternatively, in at least one of them. We focus more specifically on demonstrating superiority on at least one outcome and noninferiority (i.e., not worse) on the rest. We also advocate the more general "gatekeeping" procedures (both serial and parallel), in which primary and secondary hypotheses of interest are a priori organized into ordered sets, and testing does not proceed to the next set, i.e., through the "gate," unless the significance criteria for the previous sets are satisfied, thus protecting the overall type I error. We demonstrate methods using data from a randomized controlled trial assessing the effects of transdermal nicotine on pain and opioids after pelvic gynecological surgery. Joint hypothesis testing and gatekeeping procedures are shown to substantially improve the efficiency and interpretation of randomized and nonrandomized studies having multiple outcomes of interest.