By explicitly accounting for the interaction between importers and corrupt customs officials, the paper argues that setting trade tariff rates at a uniform level limits the ability of public officials to extract bribes from importers, and can therefore deliver higher government revenues and welfare than the optimally-set (Ramsey) tariff benchmark when corruption is pervasive. If the government’s main objective is to raise revenues at the minimum welfare cost, optimally-set tariff rates will be inversely proportional to the elasticity of demand of imports, and thus will generally differ across goods. Such a menu of tariff rates endows custom officials with the opportunity to extract rent from the importers. If officials have sufficient discretionary power, they might threaten to misclassify goods into more heavily taxed categories unless importers pay them a bribe. Because of the bribe, the effective tariff rate faced by the importing firm increases and the demand for the imported good therefore decreases. It can be easily shown that the resulting drop in import demand implies an efficiency loss as well as lower government revenues, when compared with the optimal taxation benchmark without corruption. A similar argument applies when customs officials offer to classify goods into low tariff categories in exchange for a bribe. The empirical evidence confirms that the interaction described might have significant relevance, as a robust association between standard deviation of trade tariffs – a measure of the diversification of tariff menus – and corruption emerges across countries.