Combining experimental evolution with whole-genome sequencing is now a well-established method for studying the genetics of adaptation and complex traits. In this type of work that features sexually-reproducing populations, studies consistently find that adaptation is highly polygenic and fueled by standing genetic variation. Less consistency is observed with respect to general evolutionary dynamics however; for example, investigators remain ambivalent about whether selection produces repeatable versus idiosyncratic responses, or whether small shifts in allele frequencies at many loci drive adaptation, versus selective sweeps at fewer loci. Resolving these open questions is a crucial next step as we move toward extrapolating findings from laboratory evolution experiments to populations inhabiting natural environments. We propose that subtle differences in experimental parameters between studies can influence evolutionary dynamics in meaningful ways, and here we empirically assess how one of those parameters – selection intensity – shapes these dynamics. We subject populations of outcrossing Saccharomyces cerevisiae to zero, moderate, and high ethanol stress for ~200 generations and ask: 1) does stronger selection intensity lead to greater changes in allele frequencies, and a higher likelihood of selective sweeps at sites driving adaptation; and (2) do targets of selection vary with selection intensity? We find some evidence for positive correlations between selection intensity and allele frequency change, but no evidence for more sweep-like patterns at high intensity. While we do find genomic regions that suggest some shared genetic architecture across treatments, we also identify distinct adaptive responses in each selection treatment. Combined with evidence of phenotypic trade-offs between treatments, our findings support the hypothesis that selection intensity might influence evolutionary outcomes due to pleiotropic and epistatic interactions. As such, we conclude that details of a selection regime should be a major point of consideration when attempting to generalize inferences across experimental evolution studies. Finally, our results demonstrate the importance of clearly defined controls when associating genomic changes with adaptation to specific selective pressures. Despite working with a presumably lab-adapted model system, without this element we would not have been able to distinguish between genomic responses to ethanol stress and laboratory conditions.