We reasoned that mating animals by minimising the covariance between ancestral contributions (MCAC mating) will generate less inbreeding and at least as much genetic gain as minimum-coancestry mating in breeding schemes where the animals are truncation-selected. We tested this hypothesis by stochastic simulation and compared the mating criteria in hierarchical and factorial breeding schemes, where the animals were selected based on breeding values predicted by animal-model BLUP. Random mating was included as a reference-mating criterion. We found that MCAC mating generated 4% to 8% less inbreeding than minimum-coancestry mating in the hierarchical and factorial breeding schemes without any loss in genetic gain. Moreover, it generated upto 28% less inbreeding and about 3% more genetic gain than random mating. The benefits of MCAC mating over minimum-coancestry mating are worthwhile because they can be achieved without extra costs or practical constraints. MCAC mating merely uses pedigree information to pair the animals more appropriately and is clearly a worthy alternative to minimum-coancestry mating and probably any other mating criterion. We believe, therefore, that MCAC mating should be used in breeding schemes where pedigree information is available.