This paper addresses the NP-hard problem of switching off bundled links whilst retaining the QoS provided to existing applications. We propose a fast heuristic, called Multiple Paths by Shortest Path First (MSPF), and evaluated its performance against two state-of-the-art techniques: GreenTE, and FGH. MSPF improves the energy saving on average by 5% as compared to GreenTE with only 1% CPU time. While yielding equivalent energy savings, MSPF requires only 0.35% of the running time of FGH. Finally, for Maximum Link Utilization (MLU) below 50% and delay no longer than the network diameter, MSPF reduces the power usage of the GÉANT topology by up to 91%.