We present a universal routing scheme for unweighted, undirected networks that always routes a packet along a path whose length is at most an additive factor of d more than opt (where opt is the length of an optimal path), using O(e log² n)-bit local routing tables and packet addresses, with d and e parameters of the network topology. For power-law random graphs, we demonstrate experimentally that d and e take on small values. The Thorup-Zwick universal multiplicative stretch 3 scheme has recently been suggested for routing on the Internet inter-AS graph; we argue, based on the results in this paper, that it is possible to improve worst-case performance on this graph by directly exploiting its power-law topology.