The decreased risk of transplant-related complications associated with non-myeloablative transplants expands the eligibility of transplant candidates as well as opens the possibility to evaluate non-myeloablative regimens in patients at high risk for complications with standard transplantation. Besides hematologic malignancies, allogeneic BMT has been shown to be curative in a number of debilitating hematologic diseases which may behave in a relatively indolent fashion, such as paroxysmal nocturnal hemoglobinuria (PNH) and refractory anemia (RA) or refractory anemia with ringed sideroblasts (RARS). However, the 30% risk of treatment-related mortality (TRM) with standard myeloablative allotransplantation usually precludes these patients from potentially curative therapy, because of concerns about shortening life in patients with these disorders. In this protocol we investigate non-myeloablative allogeneic peripheral blood stem cell (PBSC) transplantation in two groups of subjects where standard allogeneic transplantation is considered to have unacceptable toxicity.