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Since the first Genome-Wide Association Studies (GWAS), thousands of variant-trait associations have been discovered. However, the sample size required to detect additional variants using standard univariate association screening is increasingly prohibitive. Multi-trait GWAS offers a relevant alternative: it can improve statistical power and lead to new insights about gene function and the joint genetic architecture of human phenotypes. Although many methodological hurdles of multi-trait testing have been discussed, the strategy to select trait, among overwhelming possibilities, has been overlooked. In this study, we conducted extensive multi-trait tests using JASS (Joint Analysis of Summary Statistics) and assessed which genetic features of the analysed sets were associated with an increased detection of variants as compared to univariate screening. Our analyses identified multiple factors associated with the gain in the association detection in multi-trait tests. Together, these factors of the analysed sets are predictive of the gain of the multi-trait test (Pearson's ρ equal to 0.43 between the observed and predicted gain, P < 1.6 × 10 -60 ). Applying an alternative multi-trait approach (MTAG, multi-trait analysis of GWAS), we found that in most scenarios but particularly those with larger numbers of traits, JASS outperformed MTAG. Finally, we benchmark several strategies to select set of traits including the prevalent strategy of selecting clinically similar traits, which systematically underperformed selecting clinically heterogenous traits or selecting sets that issued from our data-driven models. This work provides a unique picture of the determinant of multi-trait GWAS statistical power and outline practical strategies for multi-trait testing., Competing Interests: Declaration of interests M.H.C. has received grant support from Bayer, unrelated to the current work.