We have introduced MTAG, a method for conducting meta-analysis of GWAS summary statistics for different traits which is robust to sample overlap. Both our theoretical and empirical results confirm that MTAG can increase the statistical power to identify trait-specific genetic associations. In our empirical application to DEP, NEUR, and SWB, we found that relative to the separate GWASs for the traits, MTAG led to substantial improvements in number of loci identified, predictive power of polygenic scores, and informativeness of a bioinformatics analysis. Table 1 summarizes the gains from MTAG across these analyses.