Effective pharmacological therapy is often inhibited by variable drug responses and adverse drug reactions. Dissecting the molecular basis of different drug responses is difficult due to complex interactions involving multiple genes, pathways, and cellular processes. We previously found a single nucleotide polymorphism within cystathionine beta-synthase (CYS4) that causes multi-drug sensitivity in a vineyard strain of Saccharomyces cerevisiae. However, not all variation was accounted for by CYS4. To identify additional genes influencing drug sensitivity, we used CYS4 as a covariate and conducted both single- and combined-cross linkage mapping. After eliminating numerous false-positive associations, we identified 16 drug-sensitivity loci, only 3 of which had been previously identified. Of 4 drug-sensitivity loci selected for validation, 2 showed replicated associations in independent crosses, and two quantitative trait genes within these regions, AQY1 and MKT1, were found to have drug-specific and background-dependent effects. Our results suggest that drug response may often depend on interactions between genes with multi-drug and drug-specific effects.