Compact Routing with Slack Mike Dinitz Given a weighted graph G=(V,E), a compact routing scheme is a distributed algorithm for forwarding packets from any source to any destination. The fundamental tradeoff is between the space used at each node and the stretch of the total route, measured by the multiplicative factor between the actual distance traveled and the length of the shortest possible route. We extend the normal definition with a slack parameter epsilon, which allows us to ignore up to epsilon*n2 of the shortest pairwise routes and give stronger guarantees on the remaining ones. We give good epsilon-slack routing schemes in a variety of standard routing models, including the labeled model and the name-independent designer-port model. We also give a lower bound that proves that such schemes do not exist in the name-independent fixed-port model. In the labeled model we also give a gracefully degrading scheme which works simultaneously for all epsilon > 0 and guarantees constant average stretch with polylog space.