This article discusses the problem of selecting free parameters of multiple testing procedures in confirmatory Phase III clinical trials with multiple objectives, including hypothesis weights and hypothesis ordering. We identify classes of multiple testing procedures that provide different interpretations of these parameters. This includes basic single-step procedures (Bonferroni procedure) that employ fixed hypothesis weights, as well as more powerful stepwise procedures (Holm, fallback, and chain procedures) that reweight the hypotheses during the testing process. We examine the behavior of different classes of multiple testing procedures in problems with unequally weighted hypotheses and a priori ordered hypotheses and provide practical guidelines for the choice of hypothesis weights and hypothesis ordering. The concepts discussed in the article are illustrated using case studies based on clinical trials with multiple endpoints, multiple dose-placebo comparisons, and multiple patient populations.