T-cell Receptor α/β Depleted Donor Lymphocyte Infusion

Inclusion Criteria: * Patients with hematologic malignancies that are candidates CD34+ selected, T-cell depleted allogeneic hematopoietic stem cell transplantation. * 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 left ventricular ejection fraction (LVEF) at rest must be 50% and must improve with exercise. * Hepatic: \< 3x upper limit of normal (ULN) AST and \< 1.5 mg/dL total serum bilirubin, unless there is congenital benign hyperbilirubinemia. 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: ≤ 1.2 mg/dL or if serum creatinine is outside the normal range, then creatinine clearance (CrCl) \> 40 mL/min (measured or calculated/estimated). * Pulmonary: asymptomatic or if symptomatic, diffusing capacity of the lungs for carbon monoxide (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: * Patients with active acute GvHD.