We study how firms react to unexpected increases in import tariffs. We identify our results from a sudden removal of American preferential tariffs applied on Argentine imports under the Generalized System of Preferences, which reflected American retaliation to a dispute over intellectual property between the two countries. Critical for identification, the tariff hike affected a third of Argentine exports enjoying preferential access in the American market, but did nothing to the other two thirds. We find that the higher tariffs reduced export participation of affected Argentine firms in the US market, whereas resilient exporters dealt with the cost increase by reshuffling their export baskets away from the products whose tariffs increased. In fact, affected firms were more likely both to drop suspended products from their export basket and to start exporting new (non-suspended) products to the US. Interestingly, the extensive margin effects carry over third markets, where policy did not change: after the policy shock, affected firms selling to the US were less likely to export to other markets. This happened, however, only for firms that also exited the American market. Those findings reveal the nuanced consequences of tariff preferences on the behavior of exporting firms, highlighting that their effect tend to spill over other products and other markets.