The popularity of diverse wireless communication systems has led to increased strains on the unlicensed spectrum. However, investigations have shown that vast portions of the licensed spectrum remain underutilized across frequency, space and time. To improve the utilization of the existing radio spectrum, cognitive radio (CR) allows a secondary system to access the licensed spectrum as long as the primary system's operation is not compromised. Two main CR transmission modes, spectrum overlay and underlay have been proposed. In the spectrum overlay mode, challenges in quality-of-service (QoS) provisioning arise due to the necessity for secondary users to vacate the channels when a primary user appears. In the underlay model, interference caused to the primary system has to be carefully managed resulting in a constraint of the secondary system's transmit power, which causes difficulty in QoS provisioning. In this paper, we propose an elastic bandwidth allocation scheme to make concurrent use of both spectrum overlay and underlay transmission modes. Different from existing hybrid transmission strategy, our scheme employ a novel softened peak interference power constraint to improve the performance of the secondary system while still granting the superior protection to the primary system transmissions. This allows the proposed scheme to achieve a superior transmission capacity in the CR network while avoiding the weaknesses of the both spectrum overlay and spectrum underlay transmission modes.