Patients undergo external beam radiotherapy (RT) to the pelvic region 5 days a week during weeks 1-5. Patients receive paclitaxel IV over 1 hour immediately followed by cisplatin concurrently with pelvic field radiotherapy on days 1, 8, 15, 22, 29, and 36. Patients undergo low-dose rate (LDR) OR high-dose rate (HDR) brachytherapy. For patients undergoing LDR brachytherapy, intracavitary implants are inserted 1 or 2 times within 3 weeks after completion of external beam RT. For patients undergoing HDR brachytherapy, intracavitary implants are inserted once a week for 5 weeks beginning during week 4 of external beam RT. Patients may receive a parametrial boost.