Patients receive oral SAHA once or twice daily on days 1-14* and paclitaxel IV over 3 hours followed by carboplatin IV over 30 minutes on day 1. Treatment repeats every 21 days for up to 6 courses in the absence of disease progression or unacceptable toxicity. Patients who have stable disease after the completion of 6 courses may receive single-agent SAHA at the discretion of the treating physician.