Recently, energy-aware routing has gained increasing popularity in the networking research community. The idea is that traffic demands are aggregated over a subset of the network links, allowing other links to be turned off to save energy. In this paper, we propose GreenRE - a new energy-aware routing model with the support of the new technique of data redundancy elimination (RE). This technique, enabled within the routers, can identify and remove repeated content from network transfers. Hence, capacity of network links are virtually increased and more traffic demands can be aggregated. Based on our real experiments on Orange Labs platform, we show that performing RE consumes some energy. Thus, while preserving connectivity and QoS, it is important to identify at which routers to enable RE and which links to turn off so that the power consumption of the network is minimized. We model the problem as an Integer Linear Program and propose a greedy heuristic algorithm. Simulations on several network topologies show that GreenRE can gain further 30% of energy savings in comparison with the traditional energy-aware routing model.