Nonmyeloablative Peripheral Blood Mobilized Hematopoietic Precursor Cell Transplantation for Sickle Cell Disease and Beta-thalassemia in People With Higher Risk of Transplant Failure

Background: \- Some sickle cell disease or beta-thalassemia can be cured with transplant. Researchers want to test a variation of transplant that uses low dose radiation and a combination of immunosuppressive drugs. They want to know if it helps a body to better accept donor stem cells. Objectives: \- To see if low dose radiation (300 rads), oral cyclophosphamide, pentostatin, and sirolimus help a body to better accept donor stem cells. Eligibility: \- People 4 and older with beta-thalassemia or sickle cell disease that can be cured with transplant, and their donors. Design: * Participants and donors will be screened with medical history, physical exam, blood test, tissue and blood typing, and bone marrow sampling. They will visit a social worker. * Donors: * may receive an intravenous (IV) tube in their groin vein. * will receive a drug injection daily for 5 or 6 days to move the blood stem cells from the bone marrow into general blood circulation. * will undergo apheresis: an IV is put into a vein in each arm. Blood is taken from one arm, a machine removes the white blood cells that contain blood stem cells, and the rest is returned through the other arm. * Participants: * may undergo red cell exchange procedure. * will remain in the hospital for about 30 days. * will receive a large IV line that can stay in their body from transplant through recovery. * will receive a dose of radiation, and transplant related drugs by mouth or IV. * will receive blood stem cells over 8 hours by IV. * will take neuropsychological tests and may complete questionnaires throughout the transplant process. * must stay near NIH for 4 months. They will visit the outpatient clinic weekly.