Eligibility Criteria:
* Diagnosis of one of the following hematological malignancies:
* CML, with 1 of the following:
* In first CP AND failed imatinib mesylate therapy, defined as failure to obtain a hematologic remission at 3 months or a major cytogenetic response (i.e., Ph+ cells \< 35%) at 6 months or demonstrated clonal evolution or disease progression during therapy
* In accelerated phase with \< 15% blasts
* In blast crisis that has entered into a second CP following induction chemotherapy
* AML, with 1 of the following:
* In second or subsequent complete remission (CR) (i.e., \< 5% blasts by morphology, no residual leukemia by flow cytometry, and absence of cytogenetic abnormalities)
* Failed primary induction chemotherapy, but subsequently entered into a CR with ≤ 2 subsequent re-induction chemotherapy treatment(s)
* In first CR with intermediate-risk or poor-risk cytogenetics
* ALL with 1 of the following:
* In second or subsequent CR
* In first CR AND presence of t(9;22)
* MDS, with the following:
* High-risk disease, defined by IPSS score of ≥ 1.5 at diagnosis AND meets 1 of the following criteria:
* ≤ 10% blasts at diagnosis
* In morphologic CR (\< 5% blasts) following cytoreductive chemotherapy
* CMML, with 1 of the following:
* ≤ 10% blasts at diagnosis
* In morphologic CR (\< 5% blasts) following cytoreductive chemotherapy
* CLL/PLL with the following:
* Rai stage I-IV disease
* Failed ≥ 1 prior chemotherapy regimen (including fludarabine phosphate) or ASCT
* Documented chemosensitive or stable, non-bulky disease prior to transplant, defined as \< 20% bone marrow involvement AND lymph node size \< 3 cm in axial diameter
* No bulky tumor masses, elevated lactate dehydrogenase (LDH), B symptoms, or progressive disease prior to transplant
* Low-grade non-Hodgkin lymphoma (NHL) (i.e., small lymphocytic lymphoma, follicular center lymphoma \[grade 1 or 2\], marginal zone lymphoma, or B-cell lymphoma), with the following criteria:
* Failed ≥ 1 prior chemotherapy regimen or ASCT
* Documented chemosensitive or stable, non-bulky disease prior to transplant, defined as \< 20% bone marrow involvement AND lymph node size \< 3 cm in axial diameter
* Received ≤ 3 prior chemotherapy regimens (monoclonal antibody therapy and involved-field radiotherapy are not considered a prior regimen)
* No bulky tumor masses, elevated LDH, B symptoms, or progressive disease prior to transplant
* Mantle cell lymphoma, with the following:
* Failed to achieve remission or recurred after either conventional chemotherapy or ASCT
* Responsive or stable disease to most recent prior therapy
* No bulky tumor masses, elevated LDH, B symptoms, or progressive disease prior to transplant
* Intermediate-grade NHL (i.e., follicular center lymphoma \[grade 3\] or diffuse large cell lymphoma), meeting the following criteria:
* Failed to achieve remission or recurred after either conventional chemotherapy or ASCT
* Documented chemosensitive, non-bulky disease prior to transplant, defined as at least a partial remission to salvage chemotherapy (≥ 50% reduction in diameter of all disease sites)
* No bulky tumor masses, elevated LDH, B symptoms, or progressive disease prior to transplant
* Hodgkin lymphoma, with the following:
* Relapsed after prior ASCT OR after ≥ 2 combination chemotherapy regimens and ineligible for ASCT
* Documented chemosensitive, non-bulky disease prior to transplant, defined as at least a partial remission to salvage chemotherapy (≥ 50% reduction in diameter of all disease sites)
* No bulky tumor masses, elevated LDH, B symptoms, or progressive disease prior to transplant
* Peripheral T-cell NHL, with the following:
* Failed to achieve remission or recurred after either conventional chemotherapy or ASCT
* Documented chemosensitive, non-bulky disease prior to transplant, defined as at least a partial remission to salvage chemotherapy (≥ 50% reduction in diameter of all disease sites)
* No bulky tumor masses, elevated LDH, B symptoms, or progressive disease prior to transplant
* Myeloproliferative syndrome with poor risk features, meeting 1 of the following criteria:
* \< 55 years old AND Lille score of 1
* Lille score of 2
* HgB \< 10 g/dL AND abnormal karyotype
* High-risk disease, with 1 of the following:
* Age 40-72 years
* Any age AND deemed to be at significantly increased risk of morbidity and death following a standard, myeloablative unrelated donor stem cell transplant (e.g., received extensive prior therapy, including ASCT)
* HLA-matched unrelated donor available, with 1 of the following:
* 8/8 match at HLA-A, B, C, or DR loci by high-resolution genotyping
* Single allelic mismatch at either the HLA-B or HLA-C loci donor by high-resolution molecular typing
* No single allelic mismatch at HLA-A or HLA-DR loci
* KPS 80-100%
* Adapted weighted Charlson Comorbidity Index \< 3
* Serum creatinine ≤ 2.0 mg/dL
* AST or ALT \< 3 times upper limit of normal (ULN)
* Total bilirubin \< 1.5 times ULN
* LVEF ≥ 45%
* DLCO \> 50%
* No hypoxia at rest with oxygen saturation \< 92% on room air (corrected with bronchodilator therapy)
* No other severe pulmonary function abnormalities
* No HIV infection
* No active hepatitis B or C infection that, in the opinion of a gastroenterologist or the transplant committee, places the patient at moderate to high risk for developing severe hepatic disease
* No active opportunistic infection (e.g., fungal pneumonia, tuberculosis, or viral infection)