Inclusion Criteria:

Patient and Donor Demographic Criteria

- Patient must be 18-45 years of age.

- Patients must have three partially HLA matched UCB units. Units identified as the HSC
source must be HLA matched at 4-6 HLA- A and B (at low to intermediate resolution)
and DRB1 (at high resolution), and the units must be HLA matched at 4-6 HLA- A, B,
DRB1 antigens with each other. Total cryopreserved HSC graft cell dose must be >2.5 x
107 nucleated cells per kilogram recipient body weight. Also, the two umbilical cord
blood (UCB) units must be ABO-matched.

- The UCB unit identified as the Treg source must be HLA matched at 4-6 HLA antigens
with the patient (without an HLA or ABO matching criterion with the UCB HSC source).

Disease Criteria

- Patients must have a hematological malignancy as listed below:

- Acute myelogenous leukemia: high risk CR1 (as evidenced by preceding
myelodysplastic syndrome (MDS), high risk cytogenetics such as those associated
with MDS or complex karyotype, or >2 cycles to obtain complete remission (CR);
second or greater CR. Must be in remission by morphology (<5% blasts within
normocellular marrow).

- Acute lymphocytic leukemia: high risk CR1 as evidenced by high risk cytogenetics
[t(9;22), t (1:19), t(4;11) or other MLL rearrangements] or > 1 cycle to obtain CR;
second or greater CR.

- Chronic myelogenous leukemia resistant to imatinib therapy

- Myelodysplasia (MDS) IPSS Int-2 or High risk (i.e. RAEB, RAEBt) or refractory anemia
with severe pancytopenia or high risk cytogenetics. Blasts must be < 10% by a
representative bone marrow aspirate morphology (otherwise induction chemotherapy to
achieve < 10% blasts is required pre-transplant).

- Advanced myelofibrosis

- Chronic lymphocytic leukemia/small lymphocytic lymphoma (CLL/SLL), marginal zone
B-cell lymphoma or follicular lymphoma that have progressed after at least two prior
therapies. Patients with bulky disease (nodal mass greater than 5 cm) should be
considered for debulking chemotherapy before transplant.

- Lymphoplasmacytic lymphoma, mantle-cell lymphoma, prolymphocytic leukemia are
eligible after initial therapy in CR1+ or PR1+.

- Large cell non-Hodgkins lymphoma (NHL) > CR2/> PR2. Patients in CR2/PR2 with initial
short remission(<6 months) are eligible.

- Lymphoblastic lymphoma, Burkitt's lymphoma, and other high-grade NHL after initial
therapy if stage III/IV in CR1/PR1 or after progression if stage I/II <1 year.

- Multiple myeloma beyond PR2. Patients with chromosome 13 abnormalities, first
response lasting less than 6 months, or β-2 microglobulin > 3 mg/L, may be considered
for this protocol after initial therapy.

- Recipients will have a Karnofsky score > 80% and have acceptable organ function ie
creatinine < 2.0, bilirubin, AST/ALT, ALP < 2 x normal, pulmonary function > 50%
normal, left ventricular ejection fraction > 45%. Note: All patients with a
creatinine > 1.2 or a history of renal dysfunction must have creatinine clearance
(must be > 40 ml/min to be eligible).

- Recipients will sign informed consent approved by the Committee on the Use of Human
Subjects at the University of Minnesota.

Exclusion Criteria:

- Pregnant or breastfeeding

- Evidence of HIV infection or known HIV positive serology

- Current active infection

- Available HLA matched sibling donor.

- CML in active blast crisis