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This letter considers a modified IEEE 802.11-based cognitive radio network where primary users (PUs) operate on a slot-by-slot basis and secondary users (SUs) try to exploit the time unused by primary users (PUs). To improve the throughput for SUs, our IEEE 802.11-based opportunistic spectrum access (OSA) allows SUs to transmit packets with variable length depending on the remaining time of the current slot. To investigate the throughput for SUs, a novel analytical model is developed. Also, analytical results are validated by extensive simulation.