INCLUSION CRITERIA

   - Has a human leukocyte antigen (HLA)-matched or single allele mismatched adult sibling
   donor or unrelated donor.

   - Acute myeloid leukemia (AML); myelodysplastic syndrome (MDS); myeloproliferative
   disease syndrome (MPD)]; chronic lymphocytic leukemia (CLL); B- or T-cell non Hodgkin
   lymphoma (NHL); Hodgkin lymphoma (HL); or chronic myelomonocytic leukemia (CMML),
   suitable for treatment with allogeneic transplant after TLI and ATG reduced intensity
   conditioning.

   - Considered at high-risk for regimen-related toxicity from fully-ablative transplant
   conditioning (therefore reduced-intensity conditioning is recommended).

   - Ability to understand and the willingness to sign a written informed consent document.
   Patients must have signed informed consent to participate in the trial.

EXCLUSION CRITERIA

   - Uncontrolled bacterial, viral or fungal infection defined as currently taking
   medication and progression of clinical symptoms.

   - Progressive hemato lymphoid malignancy despite conventional therapy.

   - Chronic myelogenous leukemia (CML).

   - Active CNS involvement of the underlying malignancy.

   - HIV positive

   - Pregnant or lactating

   - Prior malignancy (EXCEPTION: diagnosed > 5 years ago without evidence of disease, OR
   treated ≤ 5 years ago but have a greater than 50% chance of life expectancy of ≥ 5
   years for that malignancy).

   - Have a psychiatric disorder(s) or psychosocial circumstance(s) which in the opinion of
   the primary physician would place the patient at an unacceptable risk from transplant.

   - Left ventricular ejection fraction (LEVF) < 30%, or uncontrolled cardiac failure

   - Diffusing capacity of lung for carbon monoxide (DLCO) < 40% predicted

   - Total bilirubin > 3 mg/dL

   - Serum glutamic oxaloacetic transaminase (SGOT) or serum glutamic-pyruvic transaminase
   (SGPT) > 4 x upper limit of normal (ULN)

   - Creatinine > 2 mg/dL and an estimated creatinine clearance < 40 mL/min

   - Poorly-controlled hypertension despite multiple antihypertensive medications

   - Karnofsky Performance Status (KPS) < 60%