Historically, linkage mapping populations have consisted of large, randomly selected samples of progeny from a given pedigree or cell lines from a panel of radiation hybrids. We demonstrate that, to construct a map with high genome-wide marker density, it is neither necessary nor desirable to genotype all markers in every individual of a large mapping population. Instead, a reduced sample of individuals bearing complementary recombinational or radiation-induced breakpoints may be selected for genotyping subsequent markers from a large, but sparsely genotyped, mapping population. Choosing such a sample can be reduced to a discrete stochastic optimization problem for which the goal is a sample with breakpoints spaced evenly throughout the genome. We have developed several different methods for selecting such samples and have evaluated their performance on simulated and actual mapping populations, including the Lister and Dean Arabidopsis thaliana recombinant inbred population and the GeneBridge 4 human radiation hybrid panel. Our methods quickly and consistently find much-reduced samples with map resolution approaching that of the larger populations from which they are derived. This approach, which we have termed selective mapping, can facilitate the production of high-quality, high-density genome-wide linkage maps.