We introduce a new equilibrium selection mechanism for a class of symmetric coordination games. Taking advantage of the structure of these games, we assert that the equilibrium selected by this mechanism constitutes a “natural solution” in the sense that the associated expected payoff is the highest equilibrium value that can be achieved without any player having to guess how to do so. We illustrate the concept for specific examples, discuss computational issues, and then briefly conclude with a discussion about how the concept can be generalized to other coordination games.