Inclusion Criteria:

- Histologically or cytologically confirmed malignant pleural mesothelioma (MPM) of any
of the following subtypes:

- Epithelial

- Sarcomatoid

- Mixed

- Have received only 1 prior systemic chemotherapy regimen for advanced mesothelioma

- Prior intrapleural cytotoxic agents (including bleomycin) not considered
systemic chemotherapy

- Patients who are not candidates for combination chemotherapy are eligible even
if they have not received prior chemotherapy

- Unresectable disease

- Measurable disease, defined as >= 1 unidimensionally measurable lesion >= 20 mm by
conventional techniques OR >= 10 mm by spiral CT scan

- The sole site of measurable disease must not be located within the radiotherapy
port

- No known brain metastases

- ECOG performance status (PS) 0-2 OR Karnofsky PS 60-100%

- Life expectancy > 3 months

- WBC >= 3,000/mm^3

- Absolute neutrophil count >= 1,500/mm^3

- Platelet count >= 100,000/mm^3

- Bilirubin normal

- AST/ALT =< 2.5 times upper limit of normal

- Creatinine normal OR creatinine clearance >= 50 mL/min

- Not pregnant or nursing

- Negative pregnancy test

- Fertile patients must use effective double-barrier contraception for 1 week before,
during, and for >= 2 weeks after completion of study treatment

- No history of allergic reactions attributed to compounds of similar chemical or
biologic composition to PXD101

- No symptomatic congestive heart failure

- No congestive heart failure related to primary cardiac disease

- No unstable angina pectoris

- No cardiac arrhythmia

- No condition requiring anti-arrhythmic therapy

- No uncontrolled hypertension

- No myocardial infarction within the past 6 months

- No ischemic or severe valvular heart disease

- No ongoing or active infection

- No marked baseline prolongation of QT/QTc interval

- No repeated QTc interval > 500 msec

- No long QT syndrome

- No other significant cardiovascular disease

- No other uncontrolled intercurrent illness

- No psychiatric illness or social situation that would preclude study compliance

- Recovered from prior therapy

- No prior valproic acid or other known histone deacetylase (HDAC) inhibitor

- More than 3 weeks since prior chemotherapy (6 weeks for nitrosoureas or mitomycin C)

- More than 3 weeks since prior radiation therapy

- No concurrent medication that may cause torsade de pointes

- No concurrent combination antiretroviral therapy for HIV-positive patients

- No other concurrent investigational agents

- No other concurrent anticancer agents or therapies