Interest in genetic diversity within and between human populations as a way to answer questions about race has intensified in light of recent advances in genome technology. The purpose of this article is to apply a method of generalized hierarchical modeling to two DNA data sets. The first data set consists of a small sample of individuals (n = 32 total, from eight populations) who have been fully resequenced for 63 loci that encode a total of 38,534 base pairs. The second data set consists of a large sample of individuals (n = 928 total, from 46 populations) who have been genotyped at 580 loci that encode short tandem repeats. The results are clear and somewhat surprising. We see that populations differ in the amount of diversity that they harbor. The pattern of DNA diversity is one of nested subsets, such that the diversity in non-Sub-Saharan African populations is essentially a subset of the diversity found in Sub-Saharan African populations. The actual pattern of DNA diversity creates some unsettling problems for using race as meaningful genetic categories. For example, the pattern of DNA diversity implies that some populations belong to more than one race (e.g., Europeans), whereas other populations do not belong to any race at all (e.g., Sub-Saharan Africans). As Frank Livingstone noted long ago, the Linnean classification system cannot accommodate this pattern because within the system a population cannot belong to more than one named group within a taxonomic level. Am J Phys Anthropol 2009. © 2009 Wiley-Liss, Inc.