trans-eQTL mapping, we used informed subsets of variants to reduce the number of tests by one to three orders of magnitude (Supplementary Information 10 and Supplementary Table 13). We found statistical power to detect additional associations in these restricted tests, such as the test restricted to cis-eVariants. Our results indicate that ongoing increases in sample size will continue to yield additional eQTLs, both in the cis-eQTL setting, where smaller and conditionally independent effects will be identified, and in the trans-eQTL setting, where statistical power is the main limitation.