Human explanatory dialogue is an activity in which participants interactively construct explanatory models of the topic phenomenon. However, current explanation planning technology does not support such dialogue. In this paper we describe contributions in the areas of discourse planning architectures, heuristics for knowledge communication, and user interface design that take steps towards addressing this problem. First, our explanation planning architecture independently applies various constraints on the content and organization of explanation, avoiding the inflexibility and contextual assumptions of schematic discourse plans. Second, certain planning operators simulate a human explainer’s efforts to choose and incrementally develop models of the topic phenomenon. Third, dialogue occurs in the medium of a "live information" interface designed to serve as the representational medium through which the activities of the machine and human are coupled. Collectively these contributions facilitate interactive model construction in human-machine dialogue.