Our goal was to determine if examining genetic variants jointly could account for substantially more of the variance in phenotype than would be estimated by summing the results of univariate analyses. We identified several variants that jointly explain more phenotypic variance than they do individually, and three of the four tested signals replicate in independent data. Our results highlight two important lessons: (1) joint effects need to be investigated across all SNPs, not just those with main effects, and (2) it is not sufficient to look at the significance of an interaction term in a logistic regression model to determine if there is a joint effect.