Distributed hash table (DHT)-based overlay networks, represented by Pastry, CAN, and Chord, offer an administration-free and fault-tolerant application-level overlay network. While elegant from a theoretical perspective, these systems have some disadvantages. First, they rely on application-level routing, which may be inefficient with respect to network delays and bandwidth consumption. Second, they typically construct a homogeneously structured overlay even though nodes in these networks usually have varying physical connectivity and packet-forwarding capacities. In this paper, we propose two approaches for constructing an auxiliary expressway network to take advantage of the different connectivity, forwarding capacities, and availabilities of the nodes. As a result, we are able to reconcile the conflict of presenting the applications with a homogeneous structured overlay to simplify management, while at the same time taking advantage of the inherent heterogeneity of the underlying physical network to speed up routing. Our simulation results show that our expressway can achieve close to optimal routing performance (on average, 1.07 and 1.41 times optimal routing for an Internet-like topology and a large synthesized transit-stub graph, respectively) in overlay networks.