Inclusion Criteria:

          1. Patients treated on this study will have:

               1. Acute myeloid leukemia in morphologic CR not requiring treatment for their
                  disease for 6 weeks

               2. A history of AML with < 20% residual blasts after induction therapy and
                  persisting with <20% blasts for at least 8 weeks without reinduction.

               3. RA or RARS or isolated 5q- can proceed to transplant without any treatment

               4. RAEB-1, RCMD+/-RS, or MDS NOS with stable disease for 6 months (as documented by
                  serial bone marrow examinations) in the absence of any therapy but growth factors
                  or transfusion support. Patients who require treatment to "control their disease"
                  must show chemo-responsiveness

               5. CMML or RAEB-2 must demonstrate chemo-responsiveness. Chemo-responsiveness is
                  defined as a blast percentage decrease by at least 5 percentage points and there
                  must be less than 20% blasts after treatment and at the time of transplant

               6. Hodgkin or Indolent Non-Hodgkin's lymphoma

               7. Myeloma with < 5% plasma cells in the marrow

               8. Myeloproliferative disorders

               9. Aplastic Anemia

              10. A hematological or oncological disease (not listed) in which allogeneic HSCT is
                  thought to be beneficial, and the disease is chemoresponsive.

              11. Patients without clear manifestation of their disease status in terms of stage
                  and/or responsiveness should be discussed with the PI and enrollment analysis
                  should be documented in the study records.

          2. Patients must have a related donor who is HLA mismatched at 2, 3, or 4 antigens at the
             HLA-A; B; C; DR loci in the GVHD direction. (Patients with related donors who are HLA
             identical or are a 1-antigen mismatch may be treated on this therapeutic approach, but
             will have their outcomes will not be part of the statistical aims of the study (see
             Statistical Section). The HLA matched related category includes patients with a
             syngeneic donor.

          3. Patients must have had front line therapy for their disease.

          4. Patients must adequate organ function:

               1. LVEF (Left ventricular end diastolic function) of >/=45%.

               2. DLCO (Diffusing Capacity of the Lung for Carbon Monoxide ) ≥45% of predicted
                  corrected for hemoglobin, FEV-1 (forced expiratory volume at 1 second ≥50% of
                  predicted

               3. Adequate liver function as defined by a serum bilirubin <1.8, AST or ALT < 2.5X
                  upper limit of normal

               4. Creatinine Clearance of ≥ 60 mL/min

          5. HCT-CI/Age Score ≤ 5 points (Patients with greater than 5 points will be allowed for
             trial with approval of the PI and the Co-PI or his designee. This is an adjustment to
             account for healthy patients who meet the spirit of this protocol but have histories
             that result in higher than HCT-CI 5 points. An example is a patient with a solid tumor
             malignancy in their remote history (adds 3 points to HCT-CI total) where the treatment
             for the malignancy occurred years to decades before and there has been complete
             recovery of toxicities.

          6. KPS≥ 90% patients older than 70 years, KPS≥ 80% patients younger than 70 years

          7. Patients must be willing to use contraception if they have childbearing potential

        Exclusion Criteria:

          1. Performance status < 90% in patients 70 years old or greater, <80% in patients less
             than age 70 years

          2. HCT-CI/age Score >5 points (Patients with greater than 5 points will be allowed for
             trial with approval of the Principal Investigator and the Co-Principal Investigator or
             his designee. This is an adjustment to account for healthy patients who meet the
             spirit of this protocol but have histories that result in higher than HCT-CI 5 points.
             An example is a patient with a solid tumor malignancy in their remote history (adds 3
             points to HCT-CI total) where the treatment for the malignancy occurred years to
             decades before and there has been complete recovery of toxicities.

          3. A diagnosis of CMML, unless in morphologic CR

          4. HIV positive

          5. Active involvement of the central nervous system with malignancy

          6. Inability to obtain informed consent from patient or surrogate

          7. Pregnancy

          8. Patients with life expectancy of < 6 months for reasons other than their underlying
             hematologic/oncologic disorder

          9. Patients who have received alemtuzumab or antithymocyte globulin within 8 weeks of the
             transplant admission. The absence of these therapies in the medical record will serve
             as documentation that they were not given.

         10. Patients with evidence of another malignancy, exclusive of a skin cancer that requires
             only local treatment, should not be enrolled on this protocol