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 question concerns the closed-form design of scheduling policies minimizing the average transfer delay under constraints on both average and peak energies. Since, in this paper, both queue and link states may assume finite, countable infinite, or even uncountable infinite values, we cannot resort to dynamic programming to solve the aforementioned minimization problem. The key point of the (somewhat) novel approach that we follow consists of the minimization (on a per-step basis) of the queue length averaged over the fading statistics and conditioned on the queue occupancy at the previous step when two energy constraints are considered. The first one is on the allowed peak energy, and the second one is on the available average energy conditioned on the current queue occupancy. The resulting optimal scheduler operates cross layer, meaning that it allocates step-by-step energy on the basis of both current queue and link 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. The numerical tests that have been carried out corroborate these optimality properties and give insight about scheduler performance under heavy-tailed distributed input traffic, such as that generated by variable-bit-rate (VBR) media encoders.