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Adaptive modulation and diversity combining represent very important adaptive solutions for future generations of wireless communication systems. Indeed, in order to improve the performance and the efficiency of these systems, these two techniques have been recently used jointly in new schemes named joint adaptive modulation and diversity combining (JAMDC) schemes. Considering the problem of finding low hardware complexity, bandwidth-efficient, and processing-power efficient transmission schemes for a downlink scenario and capitalizing on some of these recently proposed JAMDC schemes, we propose and analyze in this paper three joint adaptive modulation, diversity combining, and power control (JAMDCPC) schemes where a constant-power variable-rate adaptive modulation technique is used with an adaptive diversity combining scheme and a common power control process. More specifically, the modulation constellation size, the number of combined diversity paths, and the needed power level are jointly determined to achieve the highest spectral efficiency with the lowest possible processing power consumption quantified in terms of the average number of combined paths, given the fading channel conditions and the required bit error rate (BER) performance. In this paper, the performance of these three JAMDCPC schemes is analyzed in terms of their spectral efficiency, processing power consumption, and error-rate performance. Selected numerical examples show that these schemes considerably increase the spectral efficiency of the existing JAMDC schemes with a slight increase in the average number of combined paths for the low signal-to-noise ratio range while maintaining compliance with the BER performance and a low radiated power which yields to a substantial decrease in interference to co-existing users and systems.