Selection of animals for breeding ranked on estimated breeding value maximizes genetic gain in the next generation but does not necessarily maximize long-term response. An alternative method, as practiced by plant breeders, is to build a desired genotype by selection on specific loci. Maximal long-term response in animal breeding requires selection on estimated breeding values with constraints on coancestry. In this paper, we compared long-term genetic response using either a genotype building or a genomic estimated breeding value (GEBV) strategy for the Australian Selection Index (ASI), a measure of profit. First, we used real marker effects from the Australian Dairy Herd Improvement Scheme to estimate breeding values for chromosome segments (approximately 25 cM long) for 2,650 Holstein bulls. Second, we selected 16 animals to be founders for a simulated breeding program where, between them, founders contain the best possible combination of 2 segments from 2 animals at each position in the genome. Third, we mated founder animals and their descendants over 30 generations with 2 breeding objectives: (1) to create a population with the "ideal genotype," where the best 2 segments from the founders segregate at each position, or (2) obtain the highest possible response in ASI with coancestry lower than that achieved under breeding objective 1. Results show that genotype building achieved the ideal genotype for breeding objective 1 and obtained a large gain in ASI over the current population (+A$864.99). However, selection on overall GEBV had greater short-term response and almost as much long-term gain (+A$820.42). When coancestry was lowered under breeding objective 2, selection on overall GEBV achieved a higher response in ASI than the genotype building strategy. Selection on overall GEBV seems more flexible in its selection decisions and was therefore better able to precisely control coancestry while maximizing ASI. We conclude that selection on overall GEBV while minimizing average coancestry is the more practical strategy for dairy cattle where selection is for highly polygenic traits, the reproductive rate is relatively low, and there is low tolerance of coancestry. The outcome may be different for traits controlled by few loci of relatively large effects or for different species. In contrast to other simulations, our results indicate that response to selection on overall GEBV may continue for several generations. This is because long-term genetic change in complex traits requires favorable changes to allele frequencies for many loci located throughout the genome.