There is mounting evidence that complex human phenotypes are highly polygenic, with many loci harboring multiple causal variants, yet most genetic association studies examine each SNP in isolation. While this has led to the discovery of thousands of disease associations, discovered variants account for only a small fraction of disease heritability. Alternative multi-SNP methods have been proposed, but issues such as multiple-testing correction, sensitivity to genotyping error, and optimization for the underlying genetic architectures remain. Here we describe a local joint-testing procedure, complete with multiple-testing correction, that leverages a genetic phenomenon we call linkage masking wherein linkage disequilibrium between SNPs hides their signal under standard association methods. We show that local joint testing on the original Wellcome Trust Case Control Consortium (WTCCC) data set leads to the discovery of 22 associated loci, 5 more than the marginal approach. These loci were later found in follow-up studies containing thousands of additional individuals. We find that these loci significantly increase the heritability explained by genome-wide significant associations in the WTCCC data set. Furthermore, we show that local joint testing in a cis-expression QTL (eQTL) study of the gEUVADIS data set increases the number of genes containing significant eQTL by 10.7% over marginal analyses. Our multiplehypothesis correction and joint-testing framework are available in a python software package called Jester, available at github.com/ brielin/Jester.KEYWORDS statistical genetics; heritability; epistasis; polygenicity; joint testing G ENETIC association studies typically take a marginal approach to analysis, investigating each SNP in isolation of all other SNPs for association with a phenotype of interest. While this method has led to the discovery of thousands of loci associated with hundreds of phenotypes (Welter et al. 2014;Eicher et al. 2015), it fails to capture the additional signal available when multiple SNPs representing independent genetic signals are examined simultaneously or when SNPs are imperfectly imputed (Wood et al. 2011). Furthermore, the hidden heritability, the difference between the heritability due to genome-wide significant associations and heritability due to genotyped variants, remains substantial (Eichler et al. 2010). In this work we investigate a local joint-testing approach to analysis of genetic data sets in which pairs of variants from the same locus are examined simultaneously for association with a phenotype. The motivation for our approach comes from the mounting evidence that complex traits are highly polygenic (Visscher et al. 2012), that causal variants are not evenly distributed across the genome (Gusev et al. 2013), that known associated loci often harbor multiple causal variants (Udler et al. 2009;Fellay et al. 2010;Trynka et al. 2011;Wood et al. 2011;Liu et al. 2012;Patsopoulos et al. 2013;Pickrell 2014), and that the underlying causal variants can be in link...