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Network survivability is a crucial requirement in high-speed optical networks. Typical approaches of providing survivability have considered the failure of a single component such as a link or a node. We motivate the need for considering double-link failures and present three loopback methods for handling such failures. In the first two methods, two edge-disjoint backup paths are computed for each link for rerouting traffic when a pair of links fails. These methods require the identification of the failed links before recovery can be completed. The third method requires the precomputation of a single backup path and does not require link identification before recovery. An algorithm that precomputes backup paths for links in order to tolerate double-link failures is then presented. Numerical results comparing the performance of our algorithm with other approaches suggest that it is possible to achieve almost 100% recovery from double-link failures with a moderate increase in backup capacity. A remarkable feature of our approach is that it is possible to trade off capacity for restorability by choosing a subset of double-link failures and designing backup paths using our algorithm for only those failure scenarios.