High concentrations of aldehydes may result in poor-quality agricultural distillate. We investigate the influence of the method of mash preparation, the initial pH of the mashes, and different yeast strains on the fermentation efficiency and concentration of aldehydes from C2 (acetaldehyde) to C7 (enanthaldehyde) in rye mashes. The tested factors were revealed to have a differentiated influence on both the process efficiency and the concentrations of aldehydes, especially in the case of the dominant acetaldehyde. Mashes obtained from steamed rye grain showed significantly higher fermentation efficiencies than those prepared by the pressureless method. Increasing the pH of the sweet mashes from 4.5 to 6.0 resulted in significantly higher concentrations of acetaldehyde, especially in the case of steamed rye grain. Moreover, an increase in the concentrations of other aldehydes, i.e., from C3 (propionaldehyde) to C5 (valer- and isovaleraldehyde) was observed. A high fermentation efficiency and the lowest acetaldehyde concentrations were obtained from steamed rye mashes with an initial pH of 4.5, fermented using the yeast strains DistilaMax GW and DistilaMax HT. DistilaMax HT yeast also provided a relatively low concentration of acetaldehyde in mashes with an initial pH in the range of 4.5–5.5 prepared by the energy-saving pressureless method.