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There are two basic approaches to allocate protection resources for fast restoration. The first allocates resources upon the arrival of each connection request; yet, it incurs significant set-up time and is often capacity-inefficient. The second approach allocates protection resources during the network configuration phase; therefore, it needs to accommodate any possible arrival pattern of connection requests, hence potentially calling for a substantial over-provisioning of resources. However, in this study we establish the feasibility of this approach. Specifically, we consider a scheme that, during the network configuration phase, constructs an (additional) low-capacity backup network. Upon a failure, traffic is rerouted through a bypass in the backup network. We establish that, with proper design, backup networks induce feasible capacity overhead. We further impose several design requirements (e.g., hop-count limits) on backup networks and their induced bypasses, and prove that, commonly, they also incur minor overhead. Motivated by these findings, we design efficient algorithms for the construction of backup networks.