High-dimensional phenotypes hold promise for richer findings in association studies, but testing of several phenotype traits aggravates the grand challenge of association studies, that of multiple testing. Several methods have recently been proposed for testing jointly all traits in a high-dimensional vector of phenotypes, with prospect of increased power to detect small effects that would be missed if tested individually. However, the methods have rarely been compared to the extent of enabling assessment of their relative merits and setting up guidelines on which method to use, and how to use it. We compare the methods on simulated data and with a real metabolomics data set comprising 137 highly correlated variables and approximately 550,000 SNPs. Applying the methods to genome-wide data with hundreds of thousands of markers inevitably requires division of the problem into manageable parts facilitating parallel processing, parts corresponding to individual genetic variants, pathways, or genes, for example. Here we utilize a straightforward formulation according to which the genome is divided into blocks of nearby correlated genetic markers, tested jointly for association with the phenotypes. This formulation is computationally feasible, reduces the number of tests, and lets the methods take advantage of combining information over several correlated variables not only on the phenotype side, but also on the genotype side. Our experiments show that canonical correlation analysis has higher power than alternative methods, while remaining computationally tractable for routine use in the GWAS setting, provided the number of samples is sufficient compared to the numbers of phenotype and genotype variables tested. Sparse canonical correlation analysis and regression models with latent confounding factors show promising performance when the number of samples is small compared to the dimensionality of the data.