The notion that damages should be multiplied by the reciprocal of the probability of punishment has been around since Bentham and is one of the basic lessons of the law and economics literature. However, the simple "1/p" multiplier turns out be inapplicable in the civil damages setting. The multiplier that brings about first-best deterrence must be chosen by striking a balance between the supply of lawsuits and the need to internalize costs. Moreover, given the costs of litigation, a multiplier that minimizes overall social costs (in contrast to achieving first-best deterrence) may need to be set at a level that effectively bars many claims. This paper derives optimal damage multipliers for a costly civil litigation system and examines the conflicting implications of deterrence and social cost minimization as objectives in the design of an optimal multiplier. An empirical application suggests that the first-best deterrence multiplier for the tort system is roughly equal to two.