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This paper derives link adaptation solutions for different wireless communications channels, maximizing the energy efficiency. These solutions account for the transmission as well as processing power consumption. The minimum energy consumption is achieved by solving an optimization problem, which we prove to be quasi-convex. We show that a convex function characterizes the average number of retransmissions when errors are due to channel noise or fading. We also derive closed-form approximations of the optimal link parameters for Rayleigh and Nakagami channels. These indicate that the target outage probability is only a function of the packet length.