During stage I, patients receive a single dose of dimesna IV over 15 minutes 7 days prior to chemotherapy. Patients then receive paclitaxel IV over 3 hours followed by dimesna IV over 15-30 minutes followed immediately by cisplatin IV over 1 hour on day 1 every 3 weeks. Patients continue courses of paclitaxel, dimesna, and cisplatin every 3 weeks in the absence of disease progression or unacceptable toxicity for up to 6 courses.