Research laboratories across the UK have been hit by the introduction of caps on visa quotas.
The Beatson Institute for Cancer Research in Glasgow was initially granted only one visa for six scientists by the new system, though its quota was increased to four this week.
Karen Vousdwen, the Beatson's director, said: "We want to carry out world-leading cancer research, which demands extremely high level of expertisse. Sometimes the best-qualified person is from outside the EEA."
The cap, which was introduced in July as part of a Conservative manifesto pledge during the General Election, has caused serious concern among the scientific community, universities and business leaders about the potential damage it could do science and industry.
The controls currently limit the number of immigrants from outside the European Economic Area (EEA) to 24,100 until April. This will then be replaced by a permanent cap, yet to be discussed by the Cabinet.