Linkage disequilibrium has been a powerful tool in identifying rare disease alleles in human populations. To date, most research has been directed to isolated populations which have undergone a bottleneck followed by rapid exponential expansion. While this strategy works well for rare diseases in which all disease alleles in the population today are clonal copies of some common ancestral allele, for common disease genes with substantial allelic heterogeneity, this approach is not predicted to work. In this paper, we describe the dynamics of linkage disequilibrium in populations which have not undergone a demographic expansion. In these populations, it is shown that genetic drift creates disequilibrium over time, while in expanded populations, the disequilibrium decays with time. We propose that common disease alleles might be more efficiently identified by drift mapping – linkage disequilibrium mapping in small, old populations of constant size where the disequilibrium is the result of genetic drift, not founder effect. Theoretical models, empirical data, and simulated population models are presented as evidence for the utility of this approach.