IP Fast Reroute techniques have been proposed to achieve fast failure recovery in just a few milliseconds. The basic idea of IP Fast Reroute is to reduce recovery time after failure by precomputing backup routes. A multiple routing configurations (MRC) algorithm has been proposed for obtaining IP Fast Reroute. MRC prepares backup configurations, which are used for finding a detour route after failures. However, this current algorithm requires too many backup configurations to recover from failures. We propose a new backup configuration computation algorithm for reducing configurations as much as possible. The basic idea is to construct a spanning tree excluding failure links in each backup configuration. We show that the effectiveness of our algorithm is especially high in large-scale power-law networks.