Allogeneic stem cell transplantation with high-dose chemotherapy affords a better chance of cure of malignant and non-malignant hematological diseases compared to autologous transplantation, because of the lack of stem cell contamination and the immune mediated graft vs. leukemia effect. Unfortunately, high-dose chemotherapy and allogeneic stem cell transplantation has a substantial treatment related mortality, that is particularly high in older patients (greater than 50 yrs of age), or in those with co-morbidities such as congestive heart disease and pulmonary disease. Patients who have pre-existing infections or who have had multiple relapses with prior chemotherapy are also at high risk. In all these groups, treatment related mortality may exceed 50%, making them ineligible for high-dose chemotherapy and allogeneic stem cell transplantation.