Guaranteed, high-quality service in a computer network often requires a single reserved path. Such a path can easily suffer from single point failures. Thus, to continuously provide the same high-quality service guarantee both before and after a link failure, each flow requires both a reserved primary path and a backup path. One solution category involves eliminating resource reservation on the backup paths, and instead, computes a posteriori good unreserved backup paths to provide strict high quality service in the event of a link failure. This paper provides a solution (AvoidPBO-S) in this category that uses good unreserved backup paths to offer the same strict service guarantee despite a link failure. Initial test results show that there is only a very small likelihood that an unreserved AvoidPBO-S backup path fails to provide the kind of service guarantee as the primary path, and that AvoidPBO-S backup paths perform well compared to other methods.