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This paper proposes a method that reduces transmit-power consumption of carrier-sense multiple-access (CSMA) networks by utilizing multiuser diversity and power control. Using this method, a terminal sends a packet at a slot if the terminal's signal-to-noise ratio (SNR) is above the threshold associated with the slot. Since the threshold value decreases as time advances, this method will make the user with the largest SNR access the shared channel; thus, a packet can be transmitted with less transmit power. The analysis under the infinite-user model shows that, as traffic load grows, the expected sum-power of the conventional CSMA network increases whereas that of the proposed method decreases.