Motivated by GATT bargaining behavior and renegotiation rules, we construct a three-country, two-good general-equilibrium model of trade and examine multilateral tariff bargaining under the constraints of non-discrimination and multilateral reciprocity. We allow for a general family of government preferences and identify bargaining outcomes that can be implemented using dominant strategy proposals for all countries. In the implementation, tariff proposals are followed by multilateral rebalancing, a sequence that is broadly consistent with observed patterns identified by Bagwell, Staiger and Yurukoglu (2016) in the bargaining records for the GATT Torquay Round. The resulting bargaining outcome is efficient relative to government preferences if and only if the initial tariff vectors position the initial world price at its politically optimal level. In symmetric settings, if the initial tariffs correspond to Nash tariffs, then the resulting bargaining outcome is efficient and ensures greater-than-Nash trade volumes and welfares for all countries. We also highlight relationships between our work and previous research that examines strategy-proof rationing rules in other economic settings.