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 trade liberalization needs not be welfare enhancing if the consumers’ capacity to gather and process information is limited. Rather, it intensifies competition for scarce consumer attention, thereby triggering wasteful advertising, and it may divert purchases to imported goods at an inefficient scale. Wasteful advertising provides scope for policy intervention in the form of an advertising tax. However, the tax instrument cannot eliminate inefficient diversion of consumer purchases to imports. Therefore, even under an optimal advertising tax, neither a fall in transport costs nor advancements in the global distribution of information need generate gains from trade in this framework.