 Women with Stage III or IV ovarian cancerprimary peritoneal cancerfallopian tube cancer that have undergone surgery with residual suboptimally cytoreduced disease suboptimal defined as 1cm disease will be eligible for treatment with one 21-day cycle of carboplatin and paclitaxel and five 21-day cycles of bevacizumab, carboplatin and paclitaxel for a total of six treatment cycles; bevacizumab treatment is delayed by one cycle to ensure adequate post-surgical healing. Subjects will be evaluated by CT scans to determine response to therapy; individuals that progress will be withdrawn from the study. The CT scan conducted after the completion of therapy will dictate the next course of action. Patients demonstrating a complete response will be maintained on bevacizumab as consolidation therapy; subjects demonstrating a partial response will continue to receive bevacizumab, carboplatin and paclitaxel. The total treatment time for patients with a clinical response following the initial 6 cycles of therapy will be 12 months. Prior to starting consolidation therapy, all patients with a complete clinical response or in those for whom surgery may result in a complete secondary cytoreduction, will be given the option of undergoing a second look surgery. The findings at surgery in combination with the CT scan will determine the response to initial therapy. The decision not to participate in the second look surgery will not affect the follow-up treatment that the patient will receive. 