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Energy Efficient Ethernet, as defined by the IEEE 802.3az standard, has shown not to be as efficient as originally expected given the large values of the transition times between the active and sleep power modes. In fact, EEE performs nearly optimal only when the link load is either very low or very high, but never at medium loads. So, in order to achieve large power savings, then it is necessary to design a flow allocation algorithm that allocates traffic demands on links that avoid medium traffic loads on links, since these are far from optimal. This work defines EEE-FA, an energy-aware flow allocation algorithm that computes the best possible route in terms of energy consumption for a given network load condition. Essentially, EEE-FA computes the K-shortest paths for a given traffic demand and evaluates the consumption impact of allocating the traffic demand on each of them, in order to further select that route with minimum energy consumption impact for a given network status. This algorithm is compared with shortest path routing and it is shown that important energy savings may be achieved, however at the expense of increasing the global network traffic load and the average number of hops per demand as a consequence of using sub-optimal (in terms of distance) routes.