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In this paper, power adaptation for direct-sequence code-division multiple-access communications that employs a successive interference cancellation (SIC) receiver is considered. The transmission power is adapted so that, with the channel variations, the received power levels of each user have appropriate disparities. Under the constraint of average transmission power, we consider two strategies in adjusting the disparity between received signal powers. With the first strategy, the average bit-error rate (BER) for a given user averaged over channel fading statistics is minimized, while with the other, the instantaneous BER is equal for all users. We find that the performance difference between the two strategies becomes negligible as the average transmission power or line-of-sight component increases. We also discuss the impact of appropriate disparity in received power levels on the BER performance of SIC receivers.