CD34+ Transplants for Leukemia and Lymphoma

Inclusion Criteria: * Malignant conditions or other life-threatening disorders correctable by transplant for which CD34+ selected, T-cell depleted allogeneic hematopoietic stem cell transplantation is indicated such as: 1. AML in 1st remission - for patients who is AML does not have 'good risk' cytogenetic features (i.e. t8:21, t 15: 17, inv16). 2. Secondary AML in 1st remission 3. AML in 1st relapse or 2nd remission 4. ALL/CLL in patient remission clinical or molecular features indicating a high risk for relapse; or ALL/CLL 2nd remission 5. CML failing to respond to or not tolerating imatinib or dasatinib in first chronic phase of disease; CML in accelerated phase, second chronic phase, or in CR after accelerated phase or blast crisis. 6. Non-Hodgkin's lymphoma with chemo responsive disease in any of the following categories: 1. Intermediate or high-grade lymphomas who have failed to achieve a first CR or have relapsed following a 1st remission who are not candidates for autologous transplants. 2. Any NHL in remission which is considered not curable with chemotherapy alone and not eligible/appropriate for autologous transplant. 7. Chronic myelomonocyte leukemia: CMML-1 and CMML-2. The following inclusion criteria are also required: * Patient's age includes from ≥18 to ≤74 years old. * Patients may be of either gender or any ethnic background. * Patients must have a Karnofsky (adult) Performance Status of at least 70% * Patients must have adequate organ function measured by: Cardiac: asymptomatic or if symptomatic then LVEF at rest must be 50% and must improve with exercise. Hepatic: \< 3x ULN AST and: s 1.5 total serum bilirubin, unless there is congenital benign hyperbilirubinemia or if the hyperbilirubinemia is directly caused by the disease in which the patient is receiving a transplant (e.g. AML Chloroma obstructing the biliary tree). Patients with higher bilirubin levels due to causes other than active liver disease is also eligible with Pl approval e.g. patients with PNH, Gilbert's disease or other hemolytic disorders. Renal: serum creatinine: s; 1.2 mg/dL or if serum creatinine is outside the normal range, then CrCl \> 30 ml/min (measured or calculated/estimated). Pulmonary: asymptomatic or if symptomatic, DLCO 50% of predicted (corrected for hemoglobin). Each patient must be willing to participate as a research subject and must sign an informed consent form. Exclusion Criteria: * Female patients who are pregnant or breast-feeding * Active viral, bacterial or fungal infection * Patient seropositive for HIV-I /II; HTLV -I /II * Presence of leukemia in the CNS