Patients with Wiskott Aldrich syndrome or other primary immunodeficiencies without manifestations of hemophagocytosis, who are over 5 years of age and using donors other than histocompatible siblings, receive busulfan IV over 2 hours every 6 hours on days -6 and -5, cyclophosphamide IV over 2 hours on days -4 and -3, total body irradiation on day -2, and ATG IV over 2 hours twice daily on days -2, -1, 2, and 3. Allogeneic bone marrow or umbilical cord blood transplantation takes place on days 0 and 1. Patients receive GVHD prophylaxis with methylprednisolone IV every 12 hours on days 2-21, oral prednisone every 12 hours on days 22-100 and then tapered off over days 101 to 128, and cyclosporine IV over 2 hours every 8-12 hours on days -3 to 100.