We tested the hypothesis that mating strategies with genomic information realise lower rates of inbreeding (δ F) than with pedigree information without compromising rates of genetic gain (δ G). We used stochastic simulation to compare δ F and δ G realised by two mating strategies with pedigree and genomic information in five breeding schemes. The two mating strategies were minimum-coancestry mating (MC) and minimising the covariance between ancestral genetic contributions (MCAC). We also simulated random mating (RAND) as a reference point. Generations were discrete. Animals were truncation-selected for a single trait that was controlled by 2000 quantitative trait loci, and the trait was observed for all selection candidates before selection. The criterion for selection was genomic-breeding values predicted by a ridge-regression model. Our results showed that MC and MCAC with genomic information realised 6% to 22% less δ F than MC and MCAC with pedigree information without compromising δ G across breeding schemes. MC and MCAC realised similar δ F and δ G. In turn, MC and MCAC with genomic information realised 28% to 44% less δ F and up to 14% higher δ G than RAND. These results indicated that MC and MCAC with genomic information are more effective than with pedigree information in controlling rates of inbreeding. This implies that genomic information should be applied to more than just prediction of breeding values in breeding schemes with truncation selection.