Inclusion Criteria

DISEASE CHARACTERISTICS:

- Histologically or cytologically confirmed diagnosis of 1 of the following:

- Acute myelogenous leukemia, meeting 1 of the following criteria:

- In first complete remission (CR), meeting 1 of the following criteria:

- Poor risk [no t(15,17), inv 16, or t(8,21)]

- Not a candidate for total body irradiation (TBI)

- Any infant in first CR

- In second CR, meeting the following criteria:

- All patients

- In more than second CR OR relapsed/refractory disease, meeting the
following criteria:

- All patients

- Blast percentage > 5% and < 25% in bone marrow (BM) at the time of
stem cell transplantation (SCT)

- Acute lymphoblastic leukemia, meeting 1 of the following criteria:

- In first CR, meeting 1 of the following criteria:

- Poor risk [t(9;22), t(4;11) AND no CR after 7-28 days of induction]

- Not a candidate for TBI

- Any infant in first CR

- In second CR, meeting the following criteria:

- All patients

- In more than second CR OR relapsed/refractory disease, meeting the
following criteria:

- All patients

- Blast percentage > 5% and < 25% in BM at the time of SCT

- Acute undifferentiated or biphenotypic leukemia, meeting the following
criteria:

- All patients

- Blast percentage > 5% and < 25% in BM at the time of SCT

- Chronic myelogenous leukemia, meeting the following criteria:

- All patients

- In first chronic phase

- Myelodysplastic syndrome, meeting 1 of the following criteria:

- Primary high risk disease

- Stage > RAEB1

- Secondary high risk disease

- All patients

- Any stage

- Juvenile myelomonocytic leukemia

- All patients

- No doubling of peripheral blast counts within a period of 2 weeks

- No active CNS disease

- HLA-compatible donor available meeting 1 of the following criteria:

- Related donor

- Genotypically or phenotypically matched at ≥ 7 or 8 of HLA-A, -B, -C and
-DRB1 alleles

- Unrelated donor meeting 1 of the following criteria:

- 8 of 8 alleles matched

- For patients < 18 years old only: 7 or 8 alleles matched with the mismatch
at only 1 HLA-A, -B, -C, or -DRB1 allele

- Two HLA-compatible unrelated cord blood (UCB) units available meeting the following
criteria:

- HLA-matched minimally at 4 of 6 HLA-A, HLA-B, and DRB1 allele

- HLA-A and HLA-B matched at intermediate resolution by molecular technique

- DRB1 allele matched at high resolution by molecular technique

- Both matched UCB units with cryopreserved nucleated cell dose ≥ 1.5 x 10^7/kg

PATIENT CHARACTERISTICS:

- Karnofsky OR Lansky performance status 70-100%

- SGOT < 2 times upper limit of normal

- Bilirubin < 1.5 mg/dL (unless there is liver disease involvement)

- Creatinine normal OR creatinine clearance > 60 mL/min

- LVEF > 50% at rest OR shortening fraction ≥ 29%

- Patients with asymptomatic pulmonary disease with no prior risk factors OR
symptomatic pulmonary disease with diffusion capacity > 50% of predicted (corrected
for hemoglobin) are eligible

- No active uncontrolled viral, bacterial, or fungal infection

- No known HIV I or II positivity

- No known human T-cell lymphotrophic virus I or II positivity

- Not pregnant or nursing

- Negative pregnancy test

- Fertile patients must use effective contraception

PRIOR CONCURRENT THERAPY:

- No hydroxyurea within the past 2 weeks

- No allogeneic or autologous stem cell transplantation within the past 6 months