Cohorts of approximately 10-20 patients receive sequentially increasing levels of post-transplant immunosuppression until a minimal (short-duration) post-transplant immunosuppression regimen is identified. The minimal post-transplant immunosuppression regimen is defined as the regimen in which ≤ 3 of 10 or ≤ 6 of 20 patients develop grade II or higher acute graft-versus-host disease AND ≤ 2 of 10 or ≤ 4 of 20 patients fail to engraft 60 days post-transplantation. Once the minimal post-transplant immunosuppression regimen is identified, an additional 10 patients are treated with that regimen.