My research is concerned with the problem of turn-taking in discourse, especially as applied to intelligent interfaces, such as advice-giving systems or software help systems. A limitation of many discourse systems is their need for explicit turn-ending signals (e.g. pressing a return key). In such systems, mid-turn interruptions are impossible, although there are practical examples of where mid-turn interruptions are highly desirable. For example, an interface agent should promptly inform the user of important pieces of information, such as a lack of disk space or the loss of network connection, especially if the user is enaged in some activity that relies on that information.