This paper examines the importance of nominal rigidity for nonlinearity and asymmetry of exchange rate pass‐through. For this purpose, we rely on company‐level data of French importing firms. We find that the well established fact that “prices rise faster than they fall,” which is characterized by the convex import price reaction function, lies primarily with the presence of nominal rigidity. Once price stickiness is controlled for, there is empirical evidence that the import price reaction function is rather concave if the linearity assumption can be rejected, indicating that firms aim primarily to protect their market share.