We find that prior to World Trade Organization membership, countries set import tariffs 9 percentage points higher on inelastically supplied imports relative to those supplied elastically. The magnitude of this effect is similar to the size of average tariffs in these countries, and market power explains more of the tariff variation than a commonly used political economy variable. Moreover, US trade restrictions not covered by the WTO are significantly higher on goods where the United States has more market power. We find strong evidence that these importers have market power and use it in setting noncooperative trade policy.