This study examines 18 transcripts from audio recordings of mediation sessions at a mediation center in the western United States to explore argumentation in the context of mediation activity. The mediation sessions involve divorced or divorcing couples attempting to create or repair a plan for child custody arrangements. The study takes a conversational argument approach and investigates what is the relationship between interaction and reasoning, how disagreement is managed, and how the mediator's contributions construct an institutionally preferred form of interactivity. The analysis shows that the mediation activity is accomplished through various dialogue activities. The article makes two claims. Firstly, argument and reasoning are constituted through interaction that imposes various constraints on what contributions are appropriate in mediation talk. Secondly, dialogue activities that mediators initiate can be considered as strategic moves that they make to achieve the institutional goal of the meeting.