Inclusion Criteria:

Patients must:

- Be between the ages of 18 and 49 years inclusive.

- Have histologically proven hematologic malignancy and must meet accepted indications
for allogeneic stem cell transplantation:

- Acute myeloid leukemia (AML): high-risk in first complete remission (CR), near
first CR (< 20% marrow blasts after induction therapy), or beyond first
remission.

- Acute lymphoblastic leukemia with high-risk features in first remission
(Philadelphia chromosome positive or other similar high-risk features), near
first CR (< 20% marrow blasts after induction therapy), or beyond first
remission.

- Chronic myeloid leukemia: in chronic phase (CP) and have failed Gleevec or are
intolerant and have signs of failing other treatments, or have history of
accelerated or blast phases. Storage of autologous peripheral blood stem cells
is recommended for this group for patients, particularly if in chronic phase.

- Non-Hodgkin’s lymphoma: aggressive histology with relapsed or primary refractory
disease and not eligible for autologous transplantation. Patients with low-grade
histology must have either failed 2 or more lines of systemic chemotherapy
including one rituximab-based regimen. Radioimmunotherapy will be considered the
equivalent of one line of chemotherapy. Excluded if prior radiotherapy to chest
or prior autologous transplantation.

- Myelodysplastic syndromes with International Prognostic Scoring System (IPSS)
score of 1.5 or greater.

- Other hematological malignancies if approved by the pipeline meeting on a case
by case basis. Must also be approved by principal investigator.

- Have no HLA-matched or 1-antigen mismatched related donors and no HLA-matched
unrelated stem cell donors, or delays involved in performing a search are likely to
be detrimental to the patient.

- Have an ECOG performance status of 0 or 1 at the time of transplant.

- Have major end organs (heart, lungs, liver, and kidneys) assessed and deemed adequate
to withstand the effects of high-dose therapy planned for this protocol.

- Have given voluntary informed consent.

Exclusion Criteria:

Patients are ineligible for this protocol if they:

- Have a co-morbid medical condition, a psychiatric condition, or organ dysfunction
that makes them at high-risk for treatment failure, for failed medical compliance, or
for regimen-related toxicity from high-dose therapy.

- Patients with any of the following will be excluded:

- Pulmonary: hemoglobin (Hb)-adjusted diffusing capacity of lung for carbon
monoxide (DLCO) < 60%, forced expiratory volume in 1 second (FEV1) < 70% of
predicted, or receive continuous supplemental oxygen;

- Cardiac: left ventricular ejection fraction (LVEF) < 50% or on any treatment for
congestive heart failure;

- Renal: serum creatinine greater than 2.0 or calculated creatinine clearance <
50 cc/min;

- Liver: ALT, AST, or serum bilirubin > 1.5 x upper limit of normal (ULN). Any
patient with elevated transaminases should have careful evaluation for the cause
and liver biopsy may be required by the principle investigator. An elevated
alkaline phosphatase should be fractionated and, if of liver origin, should be
evaluated as for transaminases.

- Are female and are pregnant, lactating, or have a positive pregnancy test.

- Have a history of previous malignancy except for non-melanoma skin cancer and in-situ
carcinoma of the cervix, unless the patient has been progression-free for > 5 years

- Are HIV positive

- Refractory malignancy: acute leukemia with greater than 30% blasts in bone marrow
unless with untreated first relapse of AML or untreated myelodysplastic syndrome
evolved to AML.

- Acute leukemia with greater than 1000 blasts/ul in peripheral blood.

- Uncontrolled central nervous system (CNS) leukemia or lymphoma.

- Prior autologous or allogeneic transplantation using a myeloablative regimen.

- Uncontrolled hypertension (systolic blood pressure [SBP] > 140, diastolic blood
pressure [DBP] > 90) or hypertension requiring > 2 drugs for good control (SBP < 130,
DBP < 90).

- Invasive mold infection that is uncontrolled or has received less than one month of
antifungal therapy.