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Theorists debate whether symmetry or asymmetry of the power balance can help bring about bargaining success. Arbitration is difficult because the 'Symmetry Theory' accepts Structuralist theoretical conventions, while the 'Asymmetry Theory' rejects such conventions. This article employs a 'Nuclear Weapons Addendum' to strengthen the Asymmetry Theory by allowing it to explain bargaining results in symmetric and asymmetric cases without dismissing Structuralist assumptions. We analyze comparative case studies of the Cuban Missile Crisis and the Intermediate-Range Nuclear Forces Treaty to argue that this modified Asymmetry Theory provides a more convincing narrative that should be considered in Structuralist discussions of international negotiation.