This paper develops a general equilibrium model that shows that a small volume of North–South trade (i.e. 2% of Northern GDP) could have caused the observed rise in the skill premium, thus resolving the ‘small trade volume paradox’ in the skill premium debate. We apply the concept of ‘trade in tasks’ of Grossman and Rossi-Hansberg to analyze the nature of North-to-South manufacturing outsourcing. As a conceptual innovation, we carefully distinguish two different implicit assumptions of the Heckscher–Ohlin model: ‘factor immobility’ versus ‘task inseparability’. We show that outsourcing, as a form of trade in tasks, essentially attains ‘task separability’ while apparently retaining factor immobility, thus rendering the traditional Heckscher–Ohlin framework obsolete for analyzing current North–South trade. We argue that this change in the nature of trade calls for new thinking in economics and public policy-making.