Serious hematologic malignancies are treated through high dose or lethal chemotherapy and/or radiation therapy conditioning regimens followed by rescue with allogeneic stem cell transplantation (allo-SCT) or autologous stem cell transplantation (ASCT). These myeloablative/lymphoablative (M/L) treatment regimens involve the elimination of both the patient's hematopoietic stem cells and T-lymphocytes, often leading to serious complications including graft versus host disease (GVHD). The claimed invention addresses some of these problems by providing a conditioning regimen that is designed to eliminate the patient's T-lymphocytes while retaining a functional population of hematopoietic stem cells (HSC). This non-myeloablative/lymphoablative (-/L) conditioning regimen involves the administration of one or more agents such as purine analogs (e.g., fludarabine), alkylating agents (e.g., bisulfan, cyclophosphamide), or anti-leukocyte globulins (e.g., anti-T lymphocyte globulin). After this, a donor-derived allogeneic stem cell preparation is administered to the patient. Patients treated according to the claimed invention develop donor-specific unresponsiveness and relatively fewer complications as compared to standard M/L conditioning regimens. The claimed methodologies should prove useful in the treatment of a number of hematologic malignancies such as chronic myelogenous leukemia, acute myelogenous leukemia, acute lymphoblastic leukemia, and non-Hodgkin's lymphoma.