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The study of human-human communication and the development of computational models for human-agent communication have diverged significantly throughout the last decade. Yet, despite frequently made claims of “super-human performance” in, e.g., speech recognition or image processing, so far, no system is able to lead a half-decent coherent conversation with a human. In this paper, we argue that we must start to re-consider the hallmarks of cooperative communication and the core capabilities that we have developed for it, and which conversational agents need to be equipped with: incremental joint co-construction and mentalizing. We base our argument on a vast body of work on human-human communication and its psychological processes that we reason to be relevant and necessary to take into account when modeling human-agent communication. We contrast those with current conceptualizations of human-agent interaction and formulate suggestions for the development of future systems.