Myeloablative Allogeneic Stem Cell Transplantation Using a Naive T-Cell Depleted Peripheral Blood Stem Cell Graft

Inclusion Criteria:

* Age 18 to 65 years.
* 8/8 or 7/8 HLA-identical matched sibling OR Allele level 8/8 (HLA-A, B, C, DRbeta1) matched unrelated donor.
* Patients with high risk ALL in first complete remission, with high risk being defined by the presence of t(4;11), t(9;22) or t(1;19) or patients presenting with extreme hyperleukocytosis (WBC\>500,000/ml) or partial remission after initial induction therapy.
* Adult patients with acute non-lymphocytic Leukemia (ANLL) in first complete remission with high-risk cytogenetics (monosomy chromosome 5 or 7, del(5q), abn(3q26), complex karyotypic abnormalities) or failure to achieve complete remission after standard induction therapy.
* All patients with ALL or ANLL in second or subsequent remission or partial remission (\<5% blasts in bone marrow as measured by flow cytometry).
* All patients with CML in chronic (failed interferon and/or Gleevec) or accelerated phase.
* Patients with myelodysplastic syndrome with International Prognostic Scoring System (IPSS) risk category of INT-1 or greater.
* Myelofibrosis with myeloid metaplasia
* Patients with severe aplastic anemia must have failed immunosuppressive therapy such as cyclosporine plus anti-thymocyte globulin.
* Patients with a history of CNS disease must have been treated and have no active CNS disease at the time of protocol treatment.
* ECOG performance status \<2
* Patients must have adequate function of other organ systems as measured by:
* Creatinine clearance (by Cockcroft Gault equation \[Appendix IV\]) \> 30ml/min. Hepatic transaminases (ALT/AST) \< 4 x normal, bilirubin \< 2.0 mg/dl.
* Pulmonary function tests demonstrating FVC and FEV1 of \>50% of predicted for age and DLCO \> 50% of predicted.
* Ejection fraction of \>45% by echocardiogram, radionuclide scan or cardiac MRI.
* Patients must be HIV negative.
* Patients must not be pregnant.

Exclusion Criteria:

* Patients with \> 5% blasts in bone marrow or peripheral circulation.
* Patients with rapidly progressive ANLL or ALL.