We consider the problem of finding low-complexity, bandwidth-efficient, and processing-power efficient transmission schemes for a downlink scenario under the framework of diversity combining. Capitalizing on recent results for joint adaptive modulation and diversity combining schemes (AMDC), we design and analyze two AMDC schemes that utilize power control to reduce the radiated power, and thus the potential interference to other systems/users. Based on knowledge of the channel fading, the proposed schemes adaptively select the signal constellation, diversity combiner structure, and transmit power level. We show that the novel schemes also provide significant average transmit power gains compared to existing joint adaptive QAM and diversity schemes. In particular, over a large signal to noise ratio range, the transmitted power is reduced by 30 - 50%, yielding a substantial decrease in interference to co-existing systems/users, while maintaining high average spectral efficiency, low combining complexity, and compliance with bit error rate constraints.