Clinical trials often compare two treatment groups on the basis of multiple endpoints. Frequently, the treatment is assumed to have a one-directional effect on each of the endpoints. In such trials the researcher is interested in establishing not only an overall treatment difference, but also on which endpoints there is a significant treatment effect. In the case where the treatment groups are assumed to have equal covariance matrices, two methods stand out in the literature: OBriens global OLS test statistic, applied in a closed testing procedure, and Westfall and Youngs (WFY) bootstrap procedure to adjust the single endpoint p-values. In this talk, we investigate further through simulation the properties of these methods. In addition, we propose and compare a hybrid of these two based on the T_max principle of Hothorn. It is concluded that individual p-value adjustments, either through the WFY bootstrap or the hybrid approach, are generally more effective in identifying treatment differences on individual endpoints. Finally, extensions to the unequal covariance matrices case are proposed and compared in a simulation study.