Long-term follow-up studies have demonstrated significant late toxicities of total body irradiation (TBI), which are most marked in children radiated at a young age. Growth failure, decline in cognitive function, and endocrine abnormalities have all been described. Good outcomes can be achieved with alkylating agents only as a preparative regimen. This plan will use a combination of busulfan and cyclophosphamide (Bu/Cy) with or without antithymocyte globulin (ATG) to reduce the late toxicities of therapy that includes TBI.