Before the start of a negotiation, the negotiating parties may try to affect the disagreement outcome of the negotiation by making socially-wasteful investments, such as purchasing weapons or asking for legal opinions. The incentives to make such investments depend on how the negotiation is conducted. We study the problem of a benevolent mediator who wishes to minimize pre-negotiation wasteful investments. Or main result is that the mediator should favor the strongest player, who has the lowest incentive to make wasteful investments. This result is robust to different specifications of the information available to the mediator. We therefore highlight a conflict between fairness and efficiency arising in negotiations.