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We propose a generalized joint power and rate adaptation scheme in direct-sequence (DS) code-division multiple-access (CDMA) communications over Nakagami fading channels. The transmission power allocated to user is proportional to Gi p, where Gi is the channel gain of user i and p is a real number, and the data rate (i.e., spreading gain) is jointly adapted so that a desired QoS is maintained. We analyze the average data rate of the proposed adaptation scheme subject to fixed average and peak transmission power constraints. Our results show that the proposed joint adaptation scheme provides a significant performance improvement over power-only and rate-only adaptation.