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We explore the advantages of intelligently dropping a small fraction of packets that arrive for transmission over a time varying wireless downlink. Without packet dropping, the optimal energy-delay tradeoff conforms to a square root tradeoff law, as shown by Berry and Gallager (2002). We show that intelligently dropping any non-zero fraction of the input rate dramatically changes this relation from a square root tradeoff law to a logarithmic tradeoff law. Further, we demonstrate an innovative algorithm for achieving this logarithmic tradeoff without requiring a-priori knowledge of arrival rates or channel probabilities. The algorithm can be implemented in real time and easily extends to yield similar performance for multi-user systems.