We investigate the impact of immigration of low skilled workers on the skill premium. According to standard theoretical predictions, we expect to find a positive relationship due to the increase in the relative supply of unskilled labour. Using data for the Italian economy between 2008 and 2013 we find no significant impact. We rationalise this puzzle by introducing matching, screening, and firm-level wages in a two-sector, two-goods closed economy. In this model, immigration causes a reduction in the relative cost of matching with unskilled labour. As a consequence, firms reduce their skill-intensity as well as the relative severity of screening skilled workers. The latter effect follows from the fact that the benefits of the screening activity accrue to a relatively smaller number of workers. The relative ability of skilled workers then declines and may compensate or offset the increase in the skill premium induced by the reduction in the skill ratio. By estimating a proxy for relative ability of the skilled, we indeed find evidence that migration flows from low and middle income countries into Italian regions have caused a reduction in the relative ability of skilled workers within sectors. We also estimate the welfare consequences of low-skill immigration.