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In cognitive radio (CR) systems, the efficiency of the primary user detection scheme directly affects the system performance. In this paper, we consider CR systems adopting quiet period for primary user detection. Specifically, we propose an enhanced quiet-period management scheme that utilizes two types of sensing intervals and two detection thresholds for energy detection, and can be used with and without feature detection. By using Markov analysis, we derive some performance measures for the system using the proposed scheme, including the channel utilization of CR systems and the detection delay of a primary user. Numerical results show that the proposed scheme heightens the maximum channel utilization of CR users, sustaining the miss-detection probability to be below the predefined value.