As the number of discovered loci carrying undesirable alleles continues to increase, culling carrier animals is not an option. Thus, we used a method that derives a genetic value for each genotype at a given locus. Using stochastic simulations, we assessed various strategies for a goat breeding program that combined two selection criteria used in a preselection step and four mating strategies between sires and dams to produce candidates for artificial insemination. Even without a strategy dedicated to reduce undesirable allele frequency, lethal alleles were purged and their frequencies slowly decreased whereas the average frequency of non-lethal alleles remained constant. Using, in a preselection step, an index including the genetic values for loci likely to carry an undesirable allele, was an efficient alternative to reduce the frequencies of nonlethal alleles and gave higher decrease for lethal alleles frequencies. After selection, the ability to control the frequencies of undesired alleles was similar across mating strategies. However, some mating strategies, based on optimizing an objective function including at least genetic values and increased inbreeding, enable to reduce undesired alleles at no or small cost for both genetic gain and increase in inbreeding.