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We consider a distributed opportunistic spectrum access (D-OSA) scenario in which multiple cognitive radio (CR) users attempt to access a channel licensed to some primary network. CR users operate on a frame-by-frame basis and need to carry out spectrum sensing at the beginning of each frame to determine whether the primary network is active or idle. Upon detecting the primary network being idle, CR users employ distributed/random-access mechanisms to transmit data. Spectrum sensing is imperfect and introduces false alarms and mis-detections. To protect primary users, it is required that the combined probability of mis-detection of all CR users must be below a specified threshold. For this, we argue that a cross-layer approach that jointly controls PHY-layer spectrum sensing and MAC-layer random access achieves significant gain in the saturated throughput of CR network. Our approach is motivated by an insightful observation, i.e., without compromising primary-user protection, allowing CR users to carry out spectrum sensing at a relatively high probability of false alarm achieves the dual benefits of reducing time spent on spectrum sensing and reducing throughput loss due to random-access collisions. Numerical results are presented to illustrate our approach.