This paper analyzes board independence and competence as distinct, but inextricably linked aspects of board effectiveness. Competent directors add shareholder value because they have better information about the quality of projects. While a CEO cares about shareholder value, he also wants his board to behave loyally to him by agreeing to projects that give him private benefits. Because many aspects of the CEO-board relationship are not contractible, the paper studies a model of relational contracts, a tool that has hitherto been rarely used in work on corporate governance. The analysis reveals a tradeoff: Inefficient loyalty is endogenously easier to obtain from a less competent board. The implied conflict of interest between shareholders and the CEO is particularly pronounced in difficult times. Fortunately, the tradeoff does not arise with respect to efficient loyalty. Several empirical predictions flow from the model, some of which explain existing empirical facts while others are new.