A fast reroute (FRR) technique is implemented at the edge of a computer network. If an edge device detects a node or link failure that prevents it from communicating with a neighboring routing domain, the edge device reroutes at least some data packets addressed to that domain to a backup edge device which, in turn, forwards the packets to the neighboring domain. The backup edge device is not permitted to reroute the packets a second time. According to the inventive technique, the edge device first identifies a group one or more possible backup edge devices and then selects at least one preferred backup edge device from the group. The edge device makes its selection based on the values of one or more metrics associated with the possible backup edge devices. The metrics are input to a novel selection algorithm that selects the preferred backup edge device(s) using a hierarchical selection process or a weighted-metric selection process, or some combination thereof.