We study the optimal composition of corporate boards. Directors can be either monitoring or advisory types. Monitoring constrains the empire-building tendency of chief executive officers (CEOs). If shareholders control the board nomination process, a non-monotonic relation ensues between agency problems and board composition. To preempt CEO entrenchment, shareholders may assemble an adviser-heavy board. If a powerful CEO influences the nomination process, this may result in a more monitor-heavy board. Regulations strengthening the monitoring role of boards can be harmful in precisely those cases in which agency problems are severe or in which CEO entrenchment is a threat to corporate governance.