REGIMEN II: Patients receive paclitaxel IV over 1 hour on days 1, 8, and 15. Patients also receive carboplatin, bevacizumab, and veliparib as in Regimen I. Treatment repeats every 21 days for 6 courses. Patients then receive bevacizumab alone on day 1. Treatment with bevacizumab repeats every 21 days for 16 courses in the absence of disease progression or unacceptable toxicity.