Experimental combo aims to boost stem cell transplant for rare blood cancers

Copied word for word from the study's registry entry, so the wording is the study team's rather than ours.

Inclusion Criteria: * Age 18 to 70 years of age. * Diagnosis of either Cutaneous T-Cell Lymphoma; T-Prolymphocytic Leukemia; T-Large Granulocytic Leukemia; T-Lymphoblastic Leukemia/lymphoma; or Peripheral T-Cell Lymphoma, Natural Killer/T-cell lymphoma for whom allogeneic stem cell transplantation is indicated. * An 10/10 or 8/8 HLA matched (high resolution typing at A, B, C, DRB1, DQ1) sibling or unrelated donor. * EF\>/= 50% on MUGA scan or Echocardiogram. * FEV1, FVC and corrected DLCO \>/= 40%. * Adequate renal function, as defined by estimated serum creatinine clearance \>/=50 ml/min (using the Cockcroft-Gault formula: creatinine clearance = \[(140-age)\*kg/(72\*serum creatinine)\] \* 0.85 if female) and/or serum creatinine \</=1.6 mg/dL. Renal function will be calculated using ideal body weight (IBW), unless a patient weights \>40% of their IBW, then adjusted body weight will be utilized. * Serum bilirubin \</= 1.5 x upper limit of normal. * SGOT and SGPT \</= 2 x upper limit of normal. * Able to sign informed consent. * Men and women of reproductive potential must agree to follow accepted birth control methods for the duration of the study. Female subject is either post-menopausal or surgically sterilized or willing to use an acceptable method of birth control (i.e., a hormonal contraceptive, intra-uterine device, diaphragm with spermicide, condom with spermicide, or abstinence) for the duration of the study. Male subject agrees to use an acceptable method for contraception for the duration of the study. Exclusion Criteria: * Patient with active CNS disease. * Pregnancy (positive Beta HCG test in a woman with child bearing potential defined as not post-menopausal for 12 months or no previous surgical sterilization) or currently breast-feeding. Pregnancy testing is not required for post-menopausal or surgically sterilized women. * Active hepatitis B, either active carrier (HBsAg +) or viremic (HBV DNA \>/=10,000 copies/mL, or \>/= 2,000 IU/mL). * Evidence of either cirrhosis or stage 3-4 liver fibrosis in patients with chronic hepatitis C or positive hepatitis C serology. * HIV infection. * Hematopoetic Transplant Co-Morbidity Index (HCT-CI) \>4 unless deemed clinically insignificant by primary investigator for patients receiving Time-Sequential Busulfan (total exposure 20000 umol-min). * Active uncontrolled bacterial, viral or fungal infections. * Exposure to other investigational drugs within 4 weeks before enrollment. * Grade \>/= 3 non-hematologic toxicity from previous therapy that has not resolved to \</= grade 1. * Radiation therapy to head and neck (excluding eyes), and internal organs of chest, abdomen or pelvis in the month prior to enrollment. * Prior whole brain irradiation. * Prior autologous SCT in the prior 12 months. * Congenital QT syndrome, QTc \>500 ms. * Myocardial infarction within 1 year of study entry. Subjects with a history of myocardial infarction between 6 and 12 months prior to study entry who are asymptomatic and have had a negative cardiac risk assessment (treadmill stress test, nuclear medicine stress test, or stress echocardiogram) since the event may participate; * Other significant EKG abnormalities including 2nd degree atrio-ventricular (AV) block type II, 3rd degree AV block, or bradycardia (ventricular rate less than 50 beats/min); * Symptomatic coronary artery disease (CAD), e.g., angina Canadian Class II-IV. In any patient in whom there is doubt, the patient should have a stress imaging study and, if abnormal, angiography to define whether or not CAD is present; * An EKG recorded at screening showing evidence of cardiac ischemia (ST depression depression of \>/= 2 mm, measured from isoelectric line to the ST segment). If in any doubt, the patient should have a stress imaging study and, if abnormal, angiography to define whether or not CAD is present; * Congestive heart failure (CHF) that meets New York Heart Association (NYHA) Class II to IV definitions and/or ejection fraction \<40% by MUGA scan or \<50% by echocardiogram and/or MRI; * A known history of sustained ventricular tachycardia (VT), ventricular fibrillation (VF), Torsade de Pointes, or cardiac arrest unless currently addressed with an automatic implantable cardioverter defibrillator (AICD); * Hypertrophic cardiomegaly or restrictive cardiomyopathy from prior treatment or other causes; * Uncontrolled hypertension, i.e., blood pressure (BP) of \>/= 160/95; patients who have a history of hypertension controlled by medication must be on a stable dose and meet all other inclusion criteria; or, * Any cardiac arrhythmia requiring an anti-arrhythmic medication (excluding stable doses of beta-blockers). * Patients taking drugs leading to significant QT prolongation where the interaction is too great to proceed with romidepsin. * Concomitant use of CYP3A4 inhibitors where the interaction is thought too great to proceed with romidepsin.