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In this paper, we study minimal power transmission of bursty sources over wireless channels with constraints on mean queuing delay. The power minimizing schedulers adapt power and rate of transmission based on the queue and channel state. We show that packet scheduling based on queue state can be used to trade queuing delay with transmission power, even on additive white Gaussian noise (AWGN) channels. Our extensive simulations show that small increases in average delay can lead to substantial savings in transmission power, thereby providing another avenue for mobile devices to save on battery power. We propose a low-complexity scheduler that has near-optimal performance. We also construct a variable-rate quadrature amplitude modulation (QAM)-based transmission scheme to show the benefits of the proposed formulation in a practical communication system. Power optimal schedulers with absolute packet delay constraints are also studied and their performance is evaluated via simulations.