In cognitive communication, dynamic sensing and opportunistic accessing enable secondary users to recognize and utilize the white spaces of the licensed bandwidth. Most present efforts focus on designing smarter channel sensing and access algorithms for secondary users to optimize the overall throughput and bandwidth utilization efficiency, without interfering with primary users communication. However, the transmission of the primary users are basically random and unpredictable, which usually makes the cognitive process complex and ineffective. In this paper, a non-uniform bandwidth allocation scheme is proposed, in order to regularize primary users bandwidth occupancy, which can in turn improve the sensing efficiency and throughput of the secondary users. The performance benefits are demonstrated analytically and verified by numerical simulations. In comparison to the conventional uniform bandwidth allocation scheme, the non-uniform scheme shows a higher sensing efficiency and spectrum utilization due to less bandwidth loss and lower sensing cost.