—It is important in communication networks to use routes that are as short as possible (i.e have low stretch) while keeping routing tables small. Recent advances in compact routing show that a stretch of 3 can be achieved while maintaining a sublinear (in the size of the network) space at each node [14]. It is also known that no routing scheme can achieve stretch less than 3 with sub-linear space for arbitrary networks. In contrast, simulations on real-life networks have indicated that stretch less than 3 can indeed be obtained using sub-linear sized routing tables[6]. In this paper, we further investigate the space-stretch tradeoffs for compact routing by analyzing a specific class of graphs and by presenting an efficient algorithm that (approximately) finds the optimum space-stretch tradeoff for any given network. We first study a popular model of random graphs, known as Bernoulli random graphs or Erd˝os-Renyi graphs, and prove that stretch less than 3 can be obtained in conju...