Selective sweeps of variation caused by fixation of major genes may have a dramatic impact on the genetic gain from background polygenic variation, particularly in the genome regions closely linked to the major gene. The response to selection can be restrained because of the reduced selection intensity and the reduced effective population size caused by the increase in frequency of the major gene. In the context of a selected population where fixation of a known major gene is desired, the question arises as to which is the optimal path of increase in frequency of the gene so that the selective sweep of variation resulting from its fixation is minimized. Using basic theoretical arguments we propose a frequency path that maximizes simultaneously the effective population size applicable to the selected background and the selection intensity on the polygenic variation by minimizing the average squared selection intensity on the major gene over generations up to a given fixation time. We also propose the use of mating between carriers and non-carriers of the major gene, in order to promote the effective recombination between the major gene and its linked polygenic background. Using a locus-based computer simulation assuming different degrees of linkage, we show that the path proposed is more effective than a similar path recently published, and that the combination of the selection and mating methods provides an efficient way to palliate the negative effects of a selective sweep.