As more studies adopt the approach of whole-genome screening, geneticists are faced with the challenge of having to interpret results from traditional approaches that were not designed for genome-scan data. Frequently, two-point analysis by the LOD method is performed to search for signals of linkage throughout the genome, for each of hundreds or even thousands of markers. This practice has raised the question of how to adjust the significance level for the fact that multiple tests are being performed. Various recommendations have been made, but no consensus has emerged. In this article, we propose a new method, the confidence-set approach, that circumvents the need to correct for the level of significance according to the number of markers tested. In the search for the gene location of a monogenic disorder, multiplicity adjustment is not needed in order to maintain the desired level of confidence. For complex diseases involving multiple genes, one needs only to adjust the level of significance according to the number of disease genes--a much smaller number than the number of markers in a genome screen-to ensure a predetermined genomewide confidence level. Furthermore, our formulation of the tests enables us to localize disease genes to small genomic regions, an extremely desirable feature that the traditional LOD method lacks. Our simulation study shows that, for sib-pair data, even when the coverage probability of the confidence set is chosen to be as high as 99%, our approach is able to implicate only the markers that are closely linked to the disease genes.