Engagement in a costly and destructive war can be understood as the "punishment" for entering a dispute. So, institutions that reduce the chance that a dispute leads to war will lower the costs of entering into a dispute. This may incentivize militarization and make more disputes emerge. We provide a simple model in which the support for unmediated peace talks, while effective in improving the chance of peace for a given distribution of military strength, ultimately leads to the emergence of more disputes and to higher incidence of conflict outbreak. Happily, we find that not all conflict resolution institutions suffer from these, apparently paradoxical, but actually quite intuitive drawbacks. We identify a form of third-party mediation inspired by the celebrated work by Myerson, and show that it can effectively broker peace in disputes once they emerge and also avoid perverse militarization incentives.