Human-computer dialogs are an important vehicle through which to produce a rich and compelling form of human-computer interaction. We view the specification of a human-computer dialog as a set of sequences of progressive interactions between a user and a computer system, and mine partially ordered sets, which correspond to mixing dialog initiative, embedded in these sets of sequences—a process we refer to as dialog mining—because partially ordered sets can be advantageously exploited to reduce the control complexity of a dialog implementation. Our mining losslessly compresses the specification of a dialog. We describe our mining algorithm and report the results of a simulation-oriented evaluation. Our algorithm is sound, and our results indicate that it can compress nearly all dialog specifications, and some to a high degree. This work is part of broader research on the specification and implementation of mixed-initiative dialogs.