Suppose that many polymorphic sites have been identified and genotyped in a region showing strong linkage with a trait. A key question of interest is which site (or combination of sites) in the region influences susceptibility to the trait. We have developed a novel statistical approach to this problem, in the context of qualitative-trait mapping, in which we use linkage data to identify the polymorphic sites whose genotypes could fully explain the observed linkage to the region. The information provided by this analysis is different from that provided by tests of either linkage or association. Our approach is based on the observation that if a particular site is the only site in the region that influences the trait, then-conditional on the genotypes at that site for the affected relatives-there should be no unexplained oversharing in the region among affected individuals. We focus on the affected sib-pair study design and develop test statistics that are variations on the usual allele-sharing methods used in linkage studies. We perform hypothesis tests and derive a confidence set for the true causal polymorphic site, under the assumption that there is only one site in the region influencing the trait. Our method is appropriate under a very general model for how the site influences the trait, including epistasis with unlinked loci, correlated environmental effects within families, and gene-environment interaction. We extend our method to larger sibships and apply it to an NIDDM1 data set.