Inclusion Criteria:

- Patients who are considered appropriate candidates for allogeneic hematopoietic stem
cell transplantation and have one of the following diagnoses:

- Acute lymphocytic leukemia in first or subsequent remission

- Acute myeloid leukemia in first or subsequent remission

- Acute lymphocytic leukemia in relapse or primary refractory disease with a
circulating blast count of no more than 10,000/mm^3

- Acute myeloid leukemia in relapse or primary refractory disease with a
circulating blast count of no more than 10,000/mm^3

- Refractory anemia with excess blasts (RAEB-1 and RAEB-2)

- Chronic myelogenous leukemia with a history of accelerated phase or blast crisis

- Patient with a human leukocyte antigen (HLA)-identical (HLA-A, B, C, and DRB1
molecularly matched) unrelated donor or related donor capable of donating PBSC

- DONOR SELECTION INCLUSION

- HLA-matched unrelated donors (HLA-A, B, C, and DRB1 matched based on high-resolution
typing) capable and willing to donate PBSC

- HLA-matched related donors >= 14 years and capable and willing to donate PBSC

Exclusion Criteria:

- Patients with central nervous system (CNS) involvement refractory to intrathecal
chemotherapy and/or standard cranial-spinal radiation

- Patients on other experimental protocols for prevention of acute GVHD

- Patients who weigh >= 60 kg must be discussed with the principal investigator prior
to enrolling on the protocol

- Patients who are human immunodeficiency virus positive (HIV+)

- Patients with uncontrolled infections for whom myeloablative hematopoietic stem cell
transplant (HCT) is considered contraindicated by the consulting infectious disease
physician

- Patients with organ dysfunction

- Renal insufficiency (creatinine > 1.5 mg/dl)

- Cardiac ejection fraction < 45%

- Diffusing capacity of the lung for carbon monoxide (DLCO) corrected < 60%

- Liver function abnormality; patients who have liver function tests (LFTs)
(including total bilirubin, aspartate aminotransferase [AST] and alanine
aminotransferase [ALT]) >= twice the upper limit of normal should be evaluated
by a gastrointestinal (GI) physician; if the GI physician considers that HCT on
protocol 2660 is contraindicated for that patient the patient will be excluded
from the protocol; patients with Gilbert's syndrome and no other known liver
function abnormality do not necessarily require GI consultation and may be
included on the protocol

- Patients with a life expectancy < 3 months from co-existing disease other than the
leukemia or RAEB

- Patients who are pregnant or breast-feeding

- Fertile patients of child bearing age unwilling to use contraception during and for
12 months post transplant

- Patients with a significant other medical conditions that would make them unsuitable
for transplant

- Patients with a known hypersensitivity to tacrolimus

- DONOR SELECTION EXCLUSION

- Donors who are HIV-1, HIV-2, human T-lymphotropic virus (HTLV)-1, HTLV-2 seropositive
or with active hepatitis B or hepatitis C virus infection

- Donors who fail eligibility requirements for donation of cells or tissue per section
21 Code of Federal Regulations (CFR) 1271 for donation of a HCT/product (P) will be
excluded unless use of the cells complies with 21 CFR 1271.65(b)(iii) (urgent medical
need) or with 21 CFR 1271.65(b)(i) (allogeneic use in a first-degree or second-degree
relative)

- Unrelated donors residing outside of the United States of America (USA)