We examine the effect of an imperfect audit and a subsequent appeals process in a standard adverse selection problem when legal or institutional restrictions impose an upper bound on penalties. We show that the imperfect audit always reduces the agent's information rent and enhances efficiency despite the limited liability. A subsequent appeals process, which allows the agent to challenge an unfavorable finding by the audit, is never optimal when it is costless. However, when the appeals process is costly, it can be optimal even if it is less accurate than the audit. Moreover, social welfare can increase as the cost of the appeals process increases.