Haldane's sieve posits that the majority of beneficial mutations that contribute to adaptation should be dominant, as these are the mutations most likely to establish and spread when rare. It has been argued, however, that if the dominance of mutations in their current and previous environments are correlated, Haldane's sieve could be eliminated. We constructed heterozygous lines of Saccharomyces cerevisiae containing single adaptive mutations obtained during exposure to the fungicide nystatin. Here we show that no clear dominance relationship exists across environments: mutations exhibited a range of dominance levels in a rich medium, yet were exclusively recessive under nystatin stress. Surprisingly, heterozygous replicates exhibited variable-onset rapid growth when exposed to nystatin. Targeted Sanger sequencing demonstrated that loss-of-heterozygosity (LOH) accounted for these growth patterns. Our experiments demonstrate that recessive beneficial mutations can avoid Haldane's sieve in clonal organisms through rapid LOH and thus contribute to rapid evolutionary adaptation.