Inclusion Criteria: 1. Patients with a)acute myeloid leukemia exclusive of patients in first complete remission with good risk cytogenetics (translocation 8,21,translocation 15, 17 or inversion 16); B)myelodysplastic syndrome; c)acute lymphocytic leukemia exclusive of patients in first remission without negative prognostic markers; d) relapsed or refractory nonHodgkin's lymphoma or Hodgkin's disease; e)relapsed or refractory multiple myeloma or f)relapsed or refractory chronic lymphocytic leukemia. 2. Patients who are considered appropriate for reduced intensity transplantation must present with at least one of the following: A. Age over 50 B. History of a prior hematopoietic stem cell transplant C. Patient with compromised organ function or comorbid conditioning such that a standard ablative transplant would be considered high risk. 3. Patients will have a related or unrelated donor matched at 5/6 or 6/6 HLA loci. 4. Patients must be greater than or equal to 18 years old, and younger than or equal to 70 years old to participate in the study. 5. Patients must have ECOG performance status of 0-2 6. Pulmonary function tests demonstrate DLCO (adjusted for Hgb)>50% predicted 7. Cardiac ejection fraction >40% 8. Laboratories: - Bilirubin less than or equal to 1.5mg/dL x ULN - AST/ALT/Alkaline Phosphatase less than or equal to 2.5x ULN - Serum creatinine less than or equal to 1.0mg/dL; if serum creatinine > 1.0MG/dL, then the estimated glomerular filtration rate (GFR) must be >60mL/min/1.73m^2 as calculated by the Modification of Diet in Renal Disease equation where Predicted GRF (ml/min/1.73m^2)=186x (serum creatinine)^1.154x(age in years)^-0.023x(0.742 if patient is female) x (1.212 if patient is black) 9. Patients with serologic evidence of hepatitis B or C exposure will undergo liver biopsy to assess for presence of active hepatitis or fibrosis and quantification of risk of proceeding with transplant. 10. All patients must be capable of understanding the investigational nature, potential risks and benefits of the study, and able to provide valid informed consent. All patients must be informed of the investigational nature of this study and must give written informed consent in accordance with institutional and federal guidelines. 11. Female patients of childbearing potential must have a negative serum pregnancy test within 2 weeks prior to enrollment. 12. Male and female patients must use an effective contraceptive method during the study and for a minimum of 6 months after study treatment Exclusion Criteria: 1. Patients who are HIV+ will be excluded. 2. Patients must not have serious intercurrent illness such as uncontrolled systemic infection or significant organ compromise which significantly increases the risk of undergoing allogeneic transplantation. 3. Pregnant and lactating women will be excluded.