There is a growing interest in discovery of internet topology at the interface level. A new generation of highly distributed measurement systems is currently being deployed. Unfortunately, the research community has not examined the problem of how to perform such measurements efficiently and in a network-friendly manner. In this paper we make two contributions toward that end. First, we show that standard topology discovery methods (e.g., skitter) are quite inefficient, repeatedly probing the same interfaces. This is a concern, because when scaled up, such methods will generate so much traffic that they will begin to resemble DDoS attacks. We measure two kinds of redundancy in probing (intra-and inter-monitor) and show that both kinds are important. We show that straightforward approaches to addressing these two kinds of redundancy must take opposite tacks, and are thus fundamentally in conflict. Our second contribution is to propose and evaluate Doubletree, an algorithm that reduces both types of redundancy simultaneously on routers and end systems. The key ideas are to exploit the treelike structure of routes to and from a single point in order to guide when to stop probing, and to probe each path by starting near its midpoint. Our results show that Doubletree can reduce both types of measurement load on the network dramatically, while permitting discovery of nearly the same set of nodes and links.