An EO phase modulator having transparent conducting oxide electrodes and an inverted rib waveguide structure is demonstrated. This new modulator geometry employs an EO polymer having an in-device r33 = 60pm/V. The measured half-wave voltage Vpi of these devices ranges from 5.3V to 11.2V for 3.8 and 1.5 mm long devices, respectively. The lowest VpiL figure-of-merit corresponds to 0.6V-cm (7.2mW-cm(2) of power length product) in a dual-drive configuration. The trade-off between Vpi, insertion loss and modulation bandwidth is systematically analyzed. An optimized high-speed structure is proposed, with numerical simulation showing that this new structure and an in-device r33 = 150pm/V, can achieve Vpi = 0.5V in a 5mm long active length with dual drive operation. The insertion loss is targeted at 6dB, and a 3dB optical modulation bandwidth can reach > 40GHz.