Ten years ago, evidence from genetics gave strong support to the "recent African origin" view of the evolution of modern humans, which posits that Homo sapiens arose as a new species in Africa and subsequently spread, leading to the extinction of other archaic human species. Subsequent data from the nuclear genome not only fail to support this model, they do not support any simple model of human demographic history. In this paper, we study a process in which the modern human phenotype originates in Africa and then advances across the world by local demic diffusion, hybridization, and natural selection. While the multiregional model of human origins posits a number of independent single locus selective sweeps, and the "out of Africa" model posits a sweep of a new species, we study the intermediate case of a phenotypic sweep. Numerical simulations of this process replicate many of the seemingly contradictory features of the genetic data, and suggest that as much as 80% of nuclear loci have assimilated genetic material from non-African archaic humans. © 2005 Elsevier Ltd. All rights reserved.