The genetic improvement of winemaking yeasts is a virtually infinite process, as the design of new strains must always cope with varied and ever-evolving production contexts. Good wine yeasts must feature both good primary traits, which are related to the overall fermentative fitness of the strain, and secondary traits, which provide accessory features augmenting its technological value. In this context, the superiority of "blind," genetic improvement techniques, as those based on the direct selection of the desired phenotype without prior knowledge of the genotype, was widely proven. Blind techniques such as adaptive evolution strategies were implemented for the enhancement of many traits of interest in the winemaking field. However, these strategies usually focus on single traits: this possibly leads to genetic tradeoff phenomena, where the selection of enhanced secondary traits might lead to sub-optimal primary fermentation traits. To circumvent this phenomenon, we applied a multi-step and strongly directed genetic improvement strategy aimed at combining a strong fermentative aptitude (primary trait) with an enhanced production of glutathione (secondary trait). We exploited the random genetic recombination associated to a library of 69 monosporic clones of strain UMCC 855 (Saccharomyces cerevisiae) to search for new candidates possessing both traits. This was achieved by consecutively applying three directional selective criteria: molybdate resistance (1), fermentative aptitude (2), and glutathione production (3). The strategy brought to the selection of strain 21T2-D58, which produces a high concentration of glutathione, comparable to that of other glutathione high-producers, still with a much greater fermentative aptitude.