What determines the bargaining power of states in international trade negotiations? The literature focuses predominantly on economic strength as the determinant of bargaining power. However, this explanation neglects the reality of modern trade, which is characterized by the globalization of production and high levels of economic interdependence. I argue that this interdependence undermines the effect of economic strength on the bargaining power of states. Specifically, I hypothesize that the effect of economic strength declines when a country's companies rely on inputs for their production from a negotiation partner because they are integrated into global value chains. The more a country's firms are dependent on a partner country, the less that country is able to coerce concessions from the partner country by bringing to bear its economic strength. To test this hypothesis, I use a dataset covering concessions on liberalization of the services sector made by 54 countries in 61 preferential trade agreements. By calculating the relative concessions of each partner, I construct a quantitative indicator of the outcome of trade negotiations. This indicator should reflect the underlying bargaining power of each negotiating party. The results of a regression analysis of these negotiation outcomes mostly support my hypotheses.