The paper analyzes the role of the structure of communication—i.e. who is talking with whom—in a coordination game. We run an experiment in a three-player game with Pareto ranked equilibria, where a pair of players has a profitable joint deviation from the Pareto-superior equilibrium. We show that specific communication structures lead to different ‘coalition-proof’ equilibria in this game. Results match the theoretical predictions. Subjects communicate and play the Pareto-superior equilibrium when communication is public. When pairs of players exchange messages privately, subjects play the Pareto-inferior equilibrium. Even in these latter cases, however, players’ beliefs and choices tend to react to messages, despite the fact that these are not credible.