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In liability lawsuits (e.g., patent infringement), a plaintiff demands compensation from a defendant, and the parties often negotiate a settlement to avoid a costly trial. Liability insurance creates bargaining leverage for the defendant in this settlement negotiation. We study the characteristics of monopoly and equilibrium contracts in settings where this leverage effect is a substantial source of value for insurance. Our results show that under adverse selection, a monopolist offers at most two contracts, which underinsure low-risk types and may inefficiently induce high-risk types to litigate. In a competitive market, only a pooling equilibrium with underinsurance may exist.