The usefulness of association studies for fine mapping loci with common susceptibility alleles for complex genetic diseases in outbred populations is unclear. We investigate this issue for a battery of tightly linked anonymous genetic markers spanning a candidate region centered around a disease locus, and study the joint behavior of chi-square statistics used to discover and to localize the disease locus. We used simulation methods based on a coalescent process with mutation, recombination, and genetic drift to examine the spatial distribution of markers with large noncentrality parameters in a case-control study design. Simulations with a disease allele at intermediate frequency, presumably representing an old mutation, tend to exhibit the largest noncentrality parameter values at markers near the disease locus. In contrast, simulations with a disease allele at low frequency, presumably representing a young mutation, often exhibit the largest noncentrality parameter values at markers scattered over the candidate region. In the former cases, sample sizes or marker densities sufficient to detect association are likely to lead to useful localization, whereas, in the latter case, localization of the disease locus within the candidate region is much less likely, regardless of the sample size or density of the map. The effects of increasing sample size or marker density are also investigated. Based upon a single marker analysis, we find that a simple strategy of choosing the marker with the smallest associated P value to begin a laboratory search for the disease locus performs adequately for a common disease allele. We also investigated a strategy of pooling nearby sites to form multiple allele markers. Using multiple degree of freedom chi-square tests for two or three nearby sites, we found no clear advantage of this form of pooling over a single marker analysis. Genet. Epidemiol. 20:432-457, 2001. Published by Wiley-Liss, 2001.