This study investigates how dispute-mediators handle impasse in the re-negotiation of divorce decrees by divorced couples. Three sources of impasse and three strategies for handling impasse are identified based on analysis of mediation transcripts. The concern here lies not so much in the disputant's arguments but in the discussion procedures dispute-mediators use to craft the disputant's argumentation into a tool to solve conflict. Their moves are understood here as a practice of reconstructing argumentative discourse that is neither naïve nor critical but reconstruction as design. Mediator's reconstruction reveals a type of communication work in contemporary societies involved in the crafting of forums and formats that mediate argumentative communication. This work is often invisible and strategic which makes its interpretation, judgment, and development a challenge for pragma-dialectical theory. How reconstruction as design can be understood is discussed by building on prior pragma-dialectical theory and research.