This protocol, in combination with a parallel study with a separate preparative regimen, will attempt to answer the question of which patients with primary immunodeficiencies need a preparative regimen and what intensity is needed. Patients will be enrolled according to disease type and donor source. The purpose of this study is to see how much chemotherapy is actually needed for the transplant to work. To be able to do this and still make the transplant work, the drugs used to temporarily weaken the immune system will be strengthened. In groups, patients will be treated with lowering doses of the busulfan to find the lowest dose of this drug that is needed to get full immune recovery. The investigators hope this regimen will result in complete immune system recovery while limiting the side effects of chemotherapy. A second purpose of this study is to track the recovery of different parts of the immune system. The investigators also want to identify whether the recovery is coming from donor stem cells or from the patient.