The Internet is an extremely complex system, and it is essential that we be able to make accurate measurements in order to understand its underlying behavior or to detect improper behavior (e.g., attacks). The reality, however, is that it is impractical to fully instrument anything but relatively small networks and impossible to even partially instrument many parts of the Internet. This paper analyzes a subset of the general monitor placement problem where the goal is to maximize the coverage of the entire universe of potential communication pairs (i.e., source and destination are randomly distributed in the mutable Internet address space). This issue arises, for example, when trying to detect/track a distributed attack. We present results from a simulation, seeded with data from skitter and RouteViews, that indicate we can monitor a packet with a high probability by monitoring relatively few points in the Internet. Our analysis suggests that the preferred strategy to place monitors should be to instrument one or two specific inter-AS links per AS for manyASes rather than deeply instrumenting a subset of the largest ASes. © 2007 IEEE.