It is possible to define conversation policies, such as communication or dialogue protocols, that are based strictly on what messages and, respectively, what performatives may follow each other. While such an approach has many practical applications, such protocols support only “local coherence” in a conversation. In a mixed-initiative dialogue between two agents cooperating on some joint task, there must be a “global coherence” in both the conversation and in the task they are trying to accomplish. Recognition of agent intentions about the joint task is essential for this global coherence, but there are further mechanisms needed to ensure that both local and global coherence are jointly maintained. This paper presents a general yet practical approach to designing, managing, and engineering agents that can engage in mixed-initiative dialogues. In this approach, we promote developing abstract task models and designing conversation policies in terms of such models.