We consider the problem of finding optimal transmission rates and power allocation under the framework of diversity combining. Capitalizing on recent results for both link adaptation schemes and adaptive combining, we design and analyze two joint link adaptation and diversity combining schemes. Based on the channel fading, the proposed schemes adaptively select both the signal constellation and diversity combiner structure. We show that the novel schemes provide significant throughput gains compared to existing joint adaptive QAM and diversity schemes. Further, contrary to previous results on power control for discrete rate link adaptation, power control does not give significant average spectral efficiency gains in this jointly adaptive setting. However, power control yields significant outage probability gains over the constant power schemes.