Throughout the 1970s, graft-versus-host disease (GVHD) was uniformly lethal in recipients of HLA-mismatched bone marrow. This major obstacle was overcome in 1980 by the introduction of rigorous T-cell depletion prior to transplantation into patients with severe combined immunodeficiency. However, in leukemia patients, the benefit of preventing GVHD was offset by graft rejection or graft failure. In this article, Yair Reisner and Massimo Martelli discuss how this problem may be overcome by intensification of the conditioning protocol in conjunction with a major increase in the dose of transplanted stem cells.