Inclusion Criteria:

1. Patients must be age 21 or younger and must have hematologic malignancies treatable
with allogeneic hematopoietic transplantation (acute and chronic leukemias,
myelodysplasia or lymphomas, see protocol for further details). Patients qualify for
this approach in four ways: 1) presence of organ system dysfunction or severe
systemic infections that significantly increase transplant related mortality with
standard myeloablative transplant regimens, 2) history of previous myeloablative
allogeneic or autologous transplantation, 3) currently in a third or higher CR
receiving an unrelated stem cell transplant, or 4) a combination of toxicities that
leads the investigator to feel that the child is at high risk (>50%) of TRM.
Patients eligible for inclusion based on consideration number 4 above cannot be
enrolled unless discussed with the study chair.

2. Organ system dysfunction: at least one of the following organ system dysfunction
criteria plus minimum organ function listed in exclusion criteria qualify a patient
for treatment on this protocol

1. Pulmonary: DLCO, FEV1 or TLC/FVC <60% predicted. Patients too young for PFTs
with suspected pulmonary toxicity should be assessed by a consulting
pulmonologist. If the pulmonologist judges the child to have moderate-severe
pulmonary disease they qualify for inclusion.

2. Renal: creatinine clearance <60ml/m/1.73m2

3. Hepatic: transaminases >4x normal or total bilirubin >2.0

4. Cardiac: all patients with suspected cardiac toxicity should undergo a cardiac
echo. If the shortening fraction (SF) is <25% a measurement of ejection
fraction must be obtained. Patients qualify for reduced intensity therapy if
the SF is <25% and the EF <50%.

3. Infections: Patients with responsive but unresolved invasive infections. These
infections may be fungal, bacterial or other opportunistic infections. Viral
infections do not meet this eligibility criteria.

4. Other patient groups at high risk for transplant related mortality: Patients with a
history of a prior allogeneic or autologous transplantation and patients who are in
CR3 or greater and receiving an unrelated stem cell transplant are also eligible for
this protocol. If the investigator feels that a patient has a combination of risk
factors that could increase their risk of transplant related mortality to >50% with
standard transplantation they may be eligible for inclusion, but such patients must
be reviewed with the protocol chairman prior to enrollment.

Exclusion Criteria:

1. Patients must be in a CR (<5% blasts on BM morphology, no active CNS disease, see
protocol) with the following exceptions:

1. AML may proceed with M2 marrow status (<20% blasts).

2. Lymphoma: residual disease must be responsive and non-bulky (<5cm largest
diameter).

3. Myelodysplasia: Patients with RA, and RAEB are eligible, but RAEB-IT patients
are only eligible if treated to <5% blasts (RA) with chemotherapy.

4. CML-BP must be treated to CR/CP2 to be eligible.

2. Females who are pregnant

3. Patients who are HIV positive or who have other progressive infections

4. Organ dysfunction: patients are ineligible for the following levels of severe organ
system dysfunction:

1. Cardiac: Ejection fraction <30%

2. Pulmonary: Receiving continuous supplementary oxygen or any of the following:
DLCO <30%, FVC/TLC < 30% or FEV1 <30%

3. Hepatic: patients will be excluded for hepatic synthetic dysfunction evidenced
by any of the following: prolongation of the prothrombin time with an INR >2.0,
total serum bilirubin >3, or transaminases >10x normal.

4. Renal: patients with a creatinine clearance <30ml/m/1.73m2 or who require
dialysis are not eligible

Donor Eligibility Criteria:

1. Related or unrelated donor who is a 6/6 HLA match at HLA-A, B, and DRB1 locus. 5/6
matches are acceptable with mismatches at class I alleles (A and B), but DRB1
mismatches are not allowed. Intermediate resolution typing of class I and high
resolution typing of class II alleles is required. (HLA-C and HLA-DQ matching is
encouraged, but not required with the ideal donor matching at 10/10 alleles.)

2. Unrelated cord blood may be used if matched at HLA-A, B and DRB1 at either 4/6, 5/6,
or 6/6 antigens. The minimum mononuclear cell dose required for eligibility is 3 x
107 mononuclear cells/kg recipient body weight (based on frozen cell dose). It is
strongly suggested that a back up unit of umbilical cord blood be reserved, though
not requested, in case of rejection.

Donors must pass required institutional and NMDP health and infectious disease screening.