The design of optimal immigration policy, particularly in the face of the spiralling demand for highly skilled workers, such as IT workers and engineers, is a topical issue in the policy debate as well as the economic literature. In this paper, we present empirical evidence from firm level data collected in 2000 on the demand in Europe for highly skilled workers in general and abroad and their determinants. Major findings are that the fraction of highly skilled recruited from the international labour market is very small, and it seems that foreign and domestic workers are very similar in terms of formal education, that is subject of specialisation, and job characteristics. We suggest an efficiency wage model that can explain why firms recruit foreign workers in small numbers and are willing to pay migrants the same wage as local workers and at the same time are willing to pay for moving costs, for example, that are specific to immigrating workers.