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Spectrum sensing is key to the realization of dynamic spectrum access. To protect primary users' communications from the interference caused by secondary users, spectrum sensing must meet the strict detectability requirements set by regulatory bodies, such as the FCC. Such strict detection requirements, however, can hardly be achieved using PHY-layer sensing techniques alone with one-time sensing by only a single sensor. In this paper, we jointly exploit two MAC-layer sensing methods-cooperative sensing and sensing scheduling- to improve spectrum sensing performance, while incurring minimum sensing overhead. While these sensing methods have been studied individually, little has been done on their combinations and the resulting benefits. Specifically, we propose to construct a profile of the primary signal's RSSs and design a simple, yet near-optimal, incumbent detection rule. Based on this constructed RSS profile, we develop an algorithm to find 1) an optimal set of sensors; 2) an optimal point at which to stop scheduling additional sensing; and 3) an optimal sensing duration for one-time sensing, so as to make a tradeoff between detection performance and sensing overhead. Our evaluation results show that the proposed sensing algorithms reduce the sensing overhead by up to 65 percent, while meeting the requirements of both false-alarm and misdetection probabilities of less than 0.01.