Neanderthals were a group of archaic hominids who occupied most of Europe and parts of western Asia from 30,000 to 300,000 years ago (KYA). They coexisted with modern humans for part of that time. Previous genetic analyses that compared the working sequence of the Neanderthal genome with the genomes of several modern humans showed that Neanderthals made a small (1-4%) contribution to the gene pool of all non-African populations. This observation was consistent with a single episode of Neanderthal admixture to the ancestors of all non-Africans, when the two groups coexisted in the Middle East 50-80 KYA. We analyzed the relationship between Neanderthals and modern humans in more detail, applying two complementary methods to the published working Neanderthal genome sequence and an extended set of long-range modern human genome sequences. We found that, consistent with the recent discovery of Meyer et al. (2012), Neanderthals contributed more DNA to modern East Asians than to modern Europeans. In addition, we found that the Masai of East Africa have a small but significant fraction of Neanderthal DNA.