We consider the problem of transmission scheduling of data over a wireless fading channel with hard deadline constraints. Our system consists of N users, each with a fixed amount of data that must be served by a common deadline. Given that, for each user, the channel fade state determines the throughput per unit of energy expended, our objective is to minimize the overall expected energy consumption while satisfying the deadline constraint. We consider both a linear and a strictly convex rate-power curve and obtain optimal solutions, based on dynamic programming (DP), and tractable approximate heuristics in both cases. For the special non-fading channel case with convex rate-power curve, an optimal solution is obtained based on the Shortest Path formulation. In the case of a linear rate-power curve, our DP solution has a nice "threshold" form; while for the convex rate-power curve we are able to obtain a heuristic algorithm with comparable performance with that of the optimal scheduling scheme.