The optimal design of immigration policy is a topical issue, both in the policy debate and the economic literature. In this paper, we present empirical evidence from a firm level dataset collected in 2000 on the demand for high-skilled workers, including foreign workers, in Europe and its determinants. Our major findings are that the fraction of high-skilled workers recruited from the international labour market is very small, and that foreign and domestic workers are very similar in terms of their formal education (measured by specialization subject) and their job characteristics. We suggest an efficiency wage model to explain why firms recruit foreign workers in small numbers, and why they are willing to pay immigrants the same wage as local workers, whilst at the same time also paying for their moving costs, despite the similar human capital profile of immigrants to domestic workers.