In our search for anonymization solutions for passive measurement data in the context of the LOBSTER passive network monitoring project, we discovered attacks against two initially promising candidates for IP address anonymization. We present a suite of three algorithms employing packet injection and frequency analysis, which can compromise individual addresses protected with prefix-preserving anonymization in multilinear time. We present two algorithms to counter our attacks. These methods support gradual release of topological information, as required by some applications. We also introduce an algorithm that strengthens some hash-based anonymization methods.