This paper introduces a model of limited consumer attention into an otherwise standard new trade theory model with love‐of‐variety preferences and heterogeneous firms. In this setting, we show that international integration needs not be welfare enhancing if the consumers' capacity to gather and process information is limited. Rather, it intensifies competition for scarce consumer attention, which causes mutual overbidding of producers in their advertising expenditures. The mutual overbidding renders advertising—which is informative in principle—wasteful and diverts purchases to imported goods at an inefficient scale. Wasteful advertising provides scope for policy intervention in the form of an advertising tax. However, if the tax instrument is not allowed to discriminate against foreign producers, it cannot eliminate inefficient diversion of consumer purchases to imports; hence it needs not be successful in securing gains from international integration in this framework.