Historical sound change has been modeled in Optimality Theory as a change in the ranking of constraints. In the simplest case, the surface effects of a constraint reranking can be stated in terms of a single traditional rewrite rule. However, there are also rerankings whose corresponding surface effects are diverse and complex, and cannot be stated as a single rule. It is this consequence of OT which I explore in this dissertation, examining conspiracies of historical sound changes in early Greek (the elimination of *j), in West Germanic (the near elimination of voiced fricatives), and in Slavic (the elimination of syllable codas).