We develop a game-theoretic model that identifies conditions under which a political executive will be satisfied with the actions of an appointee who decides whether to investigate possible legal violations. Because investigations are a necessary precondition for enforcement, the investigator exerts significant influence over whether, and the extent to which, laws are enforced. In our model, an executive can exert power over the investigator's actions only indirectly, via the threat of replacement. This threat is most effective when the investigator has preferences that diverge from those of the executive. In contrast, when the investigator and executive share similar preferences, the replacement threat can induce the investigator to behave dogmatically, contrary to the executive's interests. More subtly, we show how the replacement threat's effects on investigator behavior hinge on whether the executive is able to predict the behavior of potential replacements: an executive can sometimes gain leverage over the investigator if he can credibly threaten to replace her with a dogmatist. Our results have broad implications for the politics of regulatory enforcement in the United States and other developed democracies, and for the qualitative differences between regulation by independent investigators and less politically insulated agents.