Energy-efficient link adaptation is studied for a channel exhibiting log-normal shadow fading in addition to path loss. Both circuit power and power dissipated in the power amplifier are considered. The effective throughput per Joule of energy is maximized over transmit power and a margin for shadowing. It is demonstrated that the optimization problem can be transformed to a pair of concave maximization problems over transmit power and hadowing margin, respectively. Effective algorithms with superlinear convergence are proposed to solve these concave problems. The effects of varying the circuit power, the power amplifier inefficiency parameter or the distance between transmitter and receiver are discussed. It is shown that neglecting the shadowing component by setting the shadowing margin to zero may result in large losses in energy efficiency.