Abstract-In cognitive communication, dynamic sensing and opportunistic access 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, with the aim of optimizing the overall throughput and bandwidth utilization efficiency, under the condition of not interfering with primary users' communication. However, as the transmissions of the primary users are inherently random and unpredictable, sensing and sharing spectrum with the primary users inevitably make the cognitive process of the secondary users complex and ineffective. In this paper, a non-uniform bandwidth allocation scheme is proposed that regularizes the primary users' bandwidth occupancy pattern. The regularization is not designed to reshape the primary users's traffic, but to improve the sensing efficiency and throughput of the secondary users by optimizing the spectrum allocation. After the description of the new allocation scheme, we demonstrate its performance by theoretic analysis. Then we verify the validity of the non-uniform scheme with numerical simulations under non-fading and fading situations respectively. Through comparisons with the conventional uniform bandwidth allocation scheme, the nonuniform one shows higher sensing efficiency and better spectrum utilization due to lower sensing cost and reduced bandwidth loss.