The use of multiple testing procedures in the context of gene-set testing is an important but relatively underexposed topic. If a multiple testing method is used, this is usually a standard familywise error rate (FWER) or false discovery rate (FDR) controlling procedure in which the logical relationships that exist between the different (self-contained) hypotheses are not taken into account. Taking those relationships into account, however, can lead to more powerful variants of existing multiple testing procedures and can make summarizing and interpreting the final results easier. We will show that, from the perspective of interpretation as well as from the perspective of power improvement, FWER controlling methods are more suitable than FDR controlling methods. As an example of a possible power improvement, we suggest a modified version of the popular method by Holm, which we also implemented in the R package cherry.