In this paper, energy-efficient transmission schemes achieving maximal throughput over a finite time interval are studied in a problem setting including energy harvests, data arrivals and channel variation. The goal is to express the offline optimal policy in a way that facilitates a good online solution. We express any throughput maximizing energy efficient offline schedule (EE-TM-OFF) explicitly in terms of water levels. This allows per-slot real-time evaluation of transmit power and rate decisions, using estimates of the associated offline water levels. To compute the online power level, we construct a stochastic dynamic program that incorporates the offline optimal solution as a stochastic process. We introduce the "Immediate Fill" metric which provides a lower bound on the efficiency of any online policy with respect to the corresponding optimal offline solution. The online algorithms obtained this way exhibit performance close to the offline optimal, not only in the long run but also in short problem horizons, deeming them suitable for practical implementations.