Inclusion Criteria:

- Patients with high-risk diffuse large B cell or transformed low grade lymphoma
defined as:

- Residual disease after at least 6 cycles of anthracycline-based chemotherapy
(with residual disease defined as persistent bone marrow involvement and/or
persistent measurable lymph node or solid organ masses that are PET or gallium
avid)

- Progressive disease after at least 2 cycles of anthracycline-based chemotherapy

- Patients with an initial complete response but subsequent relapse within 6
months after completion of anthracycline-based chemotherapy

- Patients with any T-cell non-Hodgkin's lymphoma as defined as:

- Peripheral T-cell lymphoma (ALK negative PTCL-U) including PTCL-NOS, HSGD
(hepato-splenic gamma-delta TCL), AITL (angioimmunoblastic T-cell lymphoma),
EATL (enteropathy associated T-cell lymphoma), ALK-negative anaplastic large
cell lymphoma

- Any T-cell histology (except LGL) with residual disease after at least 4 cycles
of anthracycline-based chemotherapy (with residual disease defined as persistent
bone marrow involvement and/or persistent measurable lymph node or solid organ
masses that are PET or gallium avid)

- Patients with mantle cell lymphoma at any time in therapy

- Patients with "double-hit" lymphoma as characterized by the presence of concurrent
overexpression of Bcl-2 and c-myc

- Patients with Hodgkin's lymphoma that is

- Refractory to first-line therapy and at least one second line chemotherapy
regimen

- Relapsed Hodgkin's lymphoma which is refractory to at least one salvage
chemotherapy regimen.

- Patients with CLL/SLL with 17p- cytogenetic abnormality

- Age 18 years and greater

- ECOG performance status 0-2

- Ability to understand and the willingness to sign a written informed consent
document.

- Responsive disease to last therapy as determined by at least one of the following:

- At least PR by Revised Response Criteria

- At least PR by traditional Cheson Criteria

- < 10% of overall cellularity involved with disease on bone marrow biopsy for
patients with involvement of the bone marrow

- Minimum of 2 x 106 CD34+ cells / kg already collected and frozen. These stem cells
may have been collected from PBSC pheresis, bone marrow harvest, or the combination.

Exclusion Criteria:

Patients will be re-evaluated after autologous transplant prior to proceeding to
non-myeloablative transplant

- Pregnancy

- Evidence of HIV infection

- Heart failure uncontrolled by medications or ejection fraction less than 45%

- Active involvement of the CNS by lymphoma

- Inability to provide informed consent

- Previous autologous or allogeneic stem cell transplant

- Creatinine greater than 2 gm/dL or 24 hour urine creatinine clearance < 50 cc/minute
(does not have to satisfy both)

- Total bilirubin greater than 2 times the upper limit of normal except when due to
Gilbert's syndrome or hemolysis.

- Transaminases greater than 3 times the upper limit of normal

- FVC or DLCO of less than 50% of predicted (DLCO corrected for hemoglobin level)

- Already known to not possess suitably HLA-matched related or unrelated donor

Eligibility to proceed to allogeneic transplant Cannot be admitted for allogeneic
transplant earlier than 40 days and no later than 180 days after autologous stem cell
transplant.

- HLA identical (A, B, C and DR) related or unrelated donor available. HLA typing of
class I loci (HLA- A, B, C) will be based on complement dependent cytotoxicity assay
or PCR of sequence specific oligonucleotide primers (SSOP). Typing of HLA class II
(DRB1) will be based on PCR of sequence specific oligonucleotide primers (SSOP).

- No need for intravenous hydration in the previous 2 weeks

- Resolved mucositis

- Renal, cardiac, pulmonary, and hepatic function meet standard criteria for
nonmyeloablative SCT as listed below:

- Serum Cr < 2 gm/dL

- LV ejection fraction > 30% and no uncontrolled symptoms of congestive heart
failure

- DLCO > 50% of predicted value (corrected for hemoglobin)

- Transaminases < 5X the institution upper limit of normal

- Bilirubin < 3X the institution upper limit of normal except when Gilbert's
Syndrome or hemolysis is present

- ECOG PS ≤ 2

- No intravenous antimicrobials within 2 weeks

- No evidence of progressive disease, defined as a 25% increase from nadir in the sum
of the product of the diameters (SPD) of any lymph node previously identified as
abnormal prior to autologous transplant or the appearance of any new lymph node
greater than 1.5 cm in greatest diameter, new bone marrow involvement, or new solid
organ nodule greater than 1 cm in diameter. This restaging study will be performed at
least 28 days after the autologous transplant and within 60 days prior to admission
for allogeneic transplant. Status of stable disease (SD) is acceptable to proceed to
allogeneic transplant.