When we disclose information, we may also communicate information about information. The listener learns not only X but also that the speaker knows X. And the speaker also learns by speaking (for example, the speaker knows that the listener knows X). In this paper we present a series of examples where negotiators want to communciate X, but do not want to comunicate higher-order information about X. While it may be efficient for one negotiator to tell another the true consequences of failing to reach agreement, when such information is threatening or insulting it may be useful to prevent the threat or insult from becoming common knowledge. Game-theorists often model private information as the but-for cause of inefficient distributive bargaining. In these simple bargaining models, if each side's BATNA were common knowledge, the parties would instantaneously (and costlessly) reach agreement. But we show that while the lack of first-order informa
