Many moral theories do not allow for moral constraints to be violated or ignore that possibility entirely. But others have suggested–rightly, I believe–that it is an adequacy condition on a theory of morality that it recognize something like constraints while permitting us to break them occasionally. When we do so, we leave behind “moral remainders” in the form of duties of apology, restitution, and compensation. My goal is to elucidate these remainders, especially in connection with political philosophy. The latter is a domain of remainders par excellence, since it is the scene of endless trade-offs in the form, e.g., of eminent domain and redistribution. In particular, the libertarian impulse may be best explained as a sensitivity to–or an oversensitivity, as critics would have it–to the problem of moral remainders.