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We consider binary (on/off) power control strategies for transferring fixed size files (packets) over fading channels under constraints on transmit energy and transmission delay. The goal is to maximize the probability of successfully transferring the entire file. Three delay constrained scenarios are considered: infinite delay, an average delay constraint and a strict delay constraint. In the case of infinite delay tolerance, the optimal policy results in transmission only at the best channel state. It is observed that the probability of successful transfer is much higher under average delay constraints than for a strict delay constraint. In both average and strict delay constrained cases, the probabilities of success are seen increasing as the Doppler frequency increases.