During the past half century, multilateral trade liberalization has reduced tariffs to historically low levels. The Received Theory of multilateral trade agreements, based solely on terms-of-trade externalities between national governments, offers an explanation that has become the conventional wisdom among international trade theorists. But it displays two puzzles that cast doubt on its practical relevance: the Terms-of-Trade Puzzle and the Anti-Trade-Bias Puzzle. This paper examines the consistency of the implications of the Received Theory with actual trade policy. The basic conclusion is that the theory is inconsistent with reality. Furthermore, it is the role of terms-of-trade externalities — the central component of the Received Theory — that is the sole cause of this inconsistency.