The author first explains the institutions for private enforcement described by Landes and Posner, along with their arguments that these institutions produce an inefficient outcome. He then uses an explicit model of optimal punishment to show how institutions produce an inefficient outcome. He then uses an explicit model of optimal punishment to show how institutions can be designed to produce an efficient outcome. Specifically, the problem is eliminated by requiring the court to set the expected rather than the actual punishment and making the reward to the private firm the punishment net of collection costs, the fine collected not the fine paid. Since the firm has no control over expected punishment, its actions have no effect on the total output of offenses. Since the two costs that enter into the choice of an optimal punishment and probability -- enforcement costs and punishment costs -- are not internal to the private firm, its own profit maximizing behavior automatically generates the optimal combination. Using scenarios involving efficient locks, the paper demonstrates that if defensive expenditures by a potential victim affected only offenses against him and not offenses against others, the private system would generate the optimal amount of defense. Incentives for bribery inherent in such a system are explored. The appendix discusses the overenforcement theorum. Formulas and 27 footnotes are included. (Author abstract modified)