Inclusion Criteria

DISEASE CHARACTERISTICS:

- Diagnosis of one of the following hematopoietic malignancies:

- Acute lymphoblastic leukemia or myeloid leukemia with < 30% blasts in the bone
marrow

- Juvenile myelomonocytic leukemia

- Chronic myelogenous leukemia in chronic or accelerated phase

- Relapsed non-Hodgkin's or Hodgkin's lymphoma in at least partial remission

- Considered at high risk (> 30%) of toxic death with standard hematopoietic stem cell
transplantation (HSCT), as indicated by at least one of the following:

- Creatinine > 1.5 times normal OR creatinine clearance < 70 mL/min OR tubular
damage that is not corrected by cessation of chemotherapy

- DLCO < 60% of predicted OR history of prior intubation due to lung disease
(intubation for surgery excluded)

- Shortening fraction < 30%

- History of disseminated fungal infection during chemotherapy OR currently
receiving antifungal agents OR history of ≥ 2 septic episodes (confirmed by
cultures) that required ICU support

- Patients with improving fungal or other infections eligible

- Improving infection is defined as confirmed negative cultures on 2
separate occasions, at least 1 week apart, and/or stable or improving
imaging studies (e.g., CT scan) of the infected site

- Two imaging studies taken at least 2 weeks apart must show stable or
improved disease

- History of stroke or abnormal MRI/MRA OR leukoencephalopathy OR seizures that
are not fully controlled with anticonvulsants (> 2 episodes of seizures in the
preceding year or 1 episode of status epilepticus in a patient who is receiving
anticonvulsant therapy)

- History of prior significant bleeding (e.g., pulmonary, CNS, or
gastrointestinal) OR history of a clotting disorder as manifested by prior
significant thromboses (e.g., superior vena cava, inferior vena cava, or femoral
vein)

- Failed conventional therapies and not eligible for myeloablative protocols

- May have failed prior conventional HSCT

- No active CNS leukemia

- Unrelated or related donor available, meeting the following criteria:

- Matched for at least 7/8 loci by high-resolution typing

- One mismatch at A, B, or C loci allowed

- Fully matched at DRB1 locus

PATIENT CHARACTERISTICS:

- ECOG performance status (PS) 0-2 OR Karnofsky PS 60-100%

- No active/progressing viral, bacterial, protozoal, or fungal infection

- Transaminases ≤ 5 times normal (except in the presence of autoimmune liver disease)

- Shortening fraction ≥ 25%

- DLCO ≥ 40% OR pulse oximetry ≥ 85% on room air

- Glomerular filtration rate ≥ 40 mL/min

PRIOR CONCURRENT THERAPY:

- See Disease Characteristics

- Prior prolonged intensive chemotherapy (> 3 years of therapy or ≥ 3 different
chemotherapeutic protocols) allowed