Triggered by the Infostation system paradigm, next-generation wireless networks for personal communication services should be designed to transfer delay-sensitive bursty traffic flows over energy-limited buffer-equipped faded connections. In this application scenario, a still open basic question concerns the closed-form design of scheduling policies minimizing the average transfer-delay under constraints on both average and peak energies. The resulting optimal scheduler allocates step-by-step energy and rate on the basis of both current queue and channel states. We prove that, under the considered energy constraints, the scheduler retains two optimality properties. First, its stability region is the maximal admissible one. Second, the scheduler also minimizes the unconditional average queue-length (e.g., the queue-length averaged over both queue and channel state statistics).