This specification is generally directed to techniques for automatically transitioning applications—especially those that enable exchange of messages between users—into and/or out of a private state based on a variety of signals associated with the messages and/or the participants themselves. In various implementations, an ongoing message exchange thread between two or more participants operating two or more respective message exchange clients may be examined. Based at least in part on the examining, a likelihood may be determined that message(s) directed by one of the participants to another of the participants as part of the ongoing message exchange thread would be deemed private by at least a given participant of the two or more participants. A determination may be made of whether the determined likelihood satisfies one or more thresholds, and in response, one or more of the message exchange clients may be transitioned into a private state.