Inclusion Criteria:

- Age less than or equal to 21 years old; may be greater than 21 years old if a
previously treated St. Jude patient and within 3 years of completion of most recent
prior disease specific therapy.

- One of the following refractory hematologic malignancies (chemoresistant relapse or
primary induction failure) or diagnoses:

- ALL

- AML (>25% blasts in the bone marrow)

- secondary AML/MDS

- CML in accelerated phase or blast crisis

- juvenile myelomonocytic leukemia (JMML)

- myelodysplastic syndrome (MDS)

- Hodgkin or non-Hodgkin lymphoma (NHL) with residual or recurrent disease following
autologous HSCT, who are unable to undergo autologous HSCT due to chemo-resistant
disease or inability to have an acceptable quantity of tumor-free stem cells
collected (> 1 x 108 TNC/kg marrow or > 1 x 106 CD34+/kg PBS

- patients with a hematologic malignancy who have undergone prior allogeneic HSCT or
who have a co-morbid condition that in the medical opinion of medical faculty
(Division of Bone Marrow Transplantation and Cellular Therapy) makes standard
myeloablation prohibitive

- Does not have any other active malignancy other than the one for which this
transplant is indicated

- Cardiac shortening fraction greater than or equal to 25%

- For pediatric patients, creatinine clearance greater than or equal to 90 ml/min/1.73
m2 according to the Schwartz formula for estimated GFR (ml/min/1.73m2) = k*height
(cm)/serum creatinine (mg/dL). k is a proportionality constant that varies with age
and is a function of urinary creatinine clearance per unit of body size; 0.45 up to
12 months of age; 0.55 children and adolescent girls; and 0.70 for adolescent boys

- For adolescent or adult patients, serum creatinine 1.0 mg/dL; if serum creatinine
1.0 mg/dL, then the estimated glomerular filtration rate (GFR) must be 60 mL/min/1.73
m2 as calculated by the Modification of Diet in Renal Disease equation where
predicted GFR (ml/min/1.73 m2) = 186 x (serum creatinine)-1.154 x (age in
years)-0.023 x (0.742 if patient is female) x (1.212 if patient is black)

- Forced vital capacity (FVC) greater than or equal to 40% of predicted value or pulse
oximetry greater than or equal to 92% on room air.

- Karnofsky or Lansky (age-dependent) performance score of greater than or equal to 50
(See APPENDIX A)

- Does not have active acute or active chronic GVHD defined as requiring medical
therapy.

- Does not have active acute bronchiolitis obliterans (BO) or bronchiolitis obliterans
organizing pneumonia (BOOP).

- Has a suitable HLA partially matched family member donor available for stem cell
donation

- Bilirubin less than or equal to 1.5 times the upper limit of normal for age.

- Alanine aminotransferase (ALT) less than or equal to 1.5 times the upper limit of
normal for age.

- Aspartate aminotransferase (AST) less than or equal to 1.5 times the upper limit of
normal for age.

- Not pregnant (confirmed by negative serum or urine pregnancy test within 14 days
prior to enrollment).

- Not lactating

Inclusion criteria (stem cell donor):

- Partially HLA-matched family member.

- At least 18 years of age.

- HIV negative

- Not pregnant (confirmed by negative serum or urine pregnancy test within 14 days
prior to enrollment).

- Not lactating