In backbone networks, the line cards that drive the links between neighboring routers consume a large amount of energy. Since these networks are typically overprovisioned, selectively shutting down links during periods of low demand seems like a good way to reduce energy consumption. However, removing entire links from the topology often reduces capacity and connectivity too much, and leads to transient disruptions in the routing protocol. In this paper, we exploit the fact that many links in core networks are actually 'bundles' of multiple physical cables and line cards that can be shut down independently. Since identifying the optimal set of cables to shut down is an NP-complete problem, we propose several heuristics based on linear optimization techniques. We evaluate our heuristics on topology and traffic data from the Abilene backbone as well as on two synthetic topologies. The energy savings are significant, our simplest heuristic reduces energy consumption by 79% on Abilene under realistic traffic loads and bundled links consisting of five cables. Our optimization techniques run efficiently using standard optimization tools, such as the AMPL/CPLEX solver, making them a practical approach for network operators to reduce the energy consumption of their backbones.