Improving yeast tolerance to 1-butanol and isobutanol is a step toward enabling high-titer production. To identify previously unknown genetic targets leading to increased tolerance, we establish a tunable RNA interference (RNAi) screening approach. Specifically, we optimized the efficiency and tunability of RNA interference library screening in yeast, ultimately enabling downregulation efficiencies from 0 to 94 %. Using this system, we identified the Hsp70 family as a key regulator of isobutanol tolerance in a single round of screening, with downregulation of these genes conferring up to 64 % increased growth in 12 g/L isobutanol. For 1-butanol, we find through two rounds of iterative screening that the combined downregulation of alcohol dehydrogenase and enolase improves growth up to 3100 % in 10 g/L 1-butanol. Collectively, this work improves the tunability of RNAi in yeast as demonstrated by the discovery of novel effectors for these complex phenotypes.