Relative wages have been remarkably rigid for the last two decades in Danish manufacturing despite large shifts in relative employment from unskilled labor towards skilled and educated labor. Assuming capital-skill complementarity and fixed relative wages as a consequence of labor market institutions, we argue that skill upgrading is more pronounced during downturns than upturns. This prediction is supported by a high positive and significant correlation between changes in relative employment of skilled labor and changes in the unemployment rate. Furthermore, we show that international outsourcing has played an important role in explaining the shift in relative labor demand.