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This paper investigates the problem of energy-efficient transmission of data packets in a wireless network by jointly adapting to backlog and channel condition. Specifically, we consider minimum-energy scheduling problems over multiple-access channels, broadcast channels, and channels with fading, when packets of all users need to be transmitted before a deadline T. Earlier work has considered a similar setup and demonstrated significant transmission energy saving by adapting to backlog for channels that are time invariant and when transmission is restricted to time-division. For concreteness, throughout the paper, rates and powers corresponding to optimal coding over discrete-time additive white Gaussian noise (AWGN) channels are assumed. The results, however, hold for more general channels and coding schemes where the total transmitted power is convex in the transmission rates. The offline scheduling problems for all the channels considered are shown to reduce to convex optimization problems with linear constraints. An iterative algorithm, referred to as FlowRight, that finds optimal offline schedules is presented. A heuristic online algorithm that we call look-ahead water-filling, which jointly adapts to both channel fading state and backlog is described. By the use of a small buffer which introduces an almost fixed delay, this algorithm achieves a considerable reduction in energy relative to water filling solely on channel states.