Can political actors use rational strategies for political conflict when established institutions are unavailable to structure political choices because the institutions are themselves among the contested issues? In Soviet politics from 1985 to 1991, cross-cutting cleavages placed in question the possibility of any stable outcome. We argue that a multi-dimensional issue space was reduced to a single dimension, along which Mikhail Gorbachev could temporarily occupy a median, by the interaction between Gorbachev's own rhetoric and rhetorical tactics used by leaders of his nomenklatura opposition, by Boris Yeltsin as the leader of the democratic opposition, and by single-issue groups called neformaly. The match between these four players' rhetorics and the four strategic options identified by a simple spatial model offers empirical evidence that rational strategies were available despite institutional flux.