Background: We tested the premise that optimum-contribution selection with pedigree relationships to control inbreeding (POCS) realises at least as much true genetic gain as optimum-contribution selection with genomic relationships (GOCS) at the same rate of true inbreeding. Methods: We used stochastic simulation to estimate rates of true genetic gain realised by POCS and GOCS at a 0.01 rate of true inbreeding in three breeding schemes with best linear unbiased predictions of breeding values based on pedigree (PBLUP) and genomic (GBLUP) information. The three breeding schemes differed in number of matings and litter size. Selection was for a single trait with a heritability of 0.2. The trait was controlled by 7702 biallelic quantitative-trait loci (QTL) that were distributed across a 30-M genome. The genome contained 54,218 biallelic markers that were used in GOCS and GBLUP. A total of 6012 identity-by-descent loci were placed across the genome in base populations. Unique alleles at these loci were used to calculate rates of true inbreeding. Breeding schemes were run for 10 discrete generations. Selection candidates were genotyped and phenotyped before selection. Results: POCS realised more true genetic gain than GOCS at a 0.01 rate of true inbreeding in all combinations of breeding scheme and prediction method. POCS realised 14 to 33% more true genetic gain than GOCS with PBLUP in the three breeding schemes. It realised 1.5 to 5.7% more true genetic gain than GOCS with GBLUP. Conclusions: POCS realised more true genetic gain than GOCS because it managed expected genetic drift without restricting selection at QTL. By contrast, GOCS penalised changes in allele frequencies at markers that were generated by genetic drift and selection. Because these marker alleles were in linkage disequilibrium with QTL alleles, GOCS restricted changes in allele frequencies at QTL. This provides little incentive to use GOCS and highlights that we have more to learn before we can control inbreeding using genomic relationships in selective-breeding schemes. Until we can do so, POCS remains a worthy method of optimum-contribution selection because it realises more true genetic gain than GOCS at the same rate of true inbreeding.