Public mental health systems are increasingly facing demands from the criminal justice system and social services agencies to provide services and support in cases in which mental illness contributes to crime, homelessness, or poverty. In this article we analyze how policies from outside public mental health systems affect resource allocation within these systems, using examples from criminal justice. These policies use two types of mechanisms: inducing patients to consume treatment (by offering rewards or imposing penalties) and inducing clinicians to provide treatment (by creating priorities). We propose a classification of these social policies based on whether they affect demand through rewards or penalties or supply through priorities. We then relate the classification to data on patients treated in public systems to evaluate the current prevalence and potential for growth in these outside demands. These inducements impose a set of nonobvious costs on other patients who are not targeted by the policies. Furthermore, they create incentives for both patients and providers to modify their behavior in order to take advantage of rewards, avoid penalties, or better compete for resources with prioritized patients. We consider some policy implications for avoiding unintended consequences of these policies.