We consider strategic behavior in non-Coasean litigation: private disputes such that the court's judgment may influence the final allocation of rights even if transaction costs are zero. This occurs when the law prohibits otherwise-profitable efforts to contract around the court's judgment. This constraint arises in myriad contexts, including antitrust, labor law, unfair competition, and various types of public interest litigation. We show that non-Coasean disputes systematically create incentives for problematic rent-seeking behaviors: strategic investments intended to influence the outcome of litigation, and collusive ex ante settlements that enrich the parties at the public's expense. These problems arise because the parties generally have asymmetric stakes, and asymmetric stakes affect strategic behavior differently when litigation is non-Coasean. Our analysis has important normative implications concerning private settlements, and establishes a underlying economic connection between problematic settlements spanning a wide range of legal contexts.