Disease-susceptibility loci are now being mapped via genomewide scans in which a linkage statistic is computed at each of a large number of markers. Such disease-susceptibility loci may be identified via a peak in the test statistic when the latter is plotted against the genetic map. In this paper we establish, by appealing to renewal theory, that true positive peaks are expected to be longer than false positive peaks. These results are verified by a realistic simulation of a genomewide linkage study based on the affected-sib-pair design. Since longer peaks are more likely to contain a gene of interest than are shorter peaks, these differences may aid in linkage mapping, justifying assignment of lower priority to shorter peaks. However, since these differences are generally small, statistics based on both peak length and height may not be much more powerful than those based on height alone. The results presented here also provide a theoretical framework for methods that use the length of shared haplotypes in populations to map disease genes.