The recent availability of large scale data sets profiling single nucleotide polymorphisms (SNPs) and gene expression across different human populations, has directed much attention towards discovering patterns of genetic variation and their association with gene regulation. The influence of environmental, developmental and other factors on gene expression can obscure such associations. We present a model that explicitly accounts for non-genetic factors so as to improve significantly the power of an expression Quantitative Trait Loci (eQTL) study. Our method also exploits the inherent block structure of haplotype data to further enhance its sensitivity. On data from the HapMap project, we find more than three times as many significant associations than a standard eQTL method.