Can migration be Pareto optimal?

Immigration policy is a continuous hot potato, probably because there are winners and losers from any change. Could we then not devise some compensation scheme so as to obtain a Pareto improvement? Clearly, migrants benefits from moving, as they chose to move. In the receiving country, some gain, some lose, but on can assume that on aggregate the country wins, as it lets people in, but not too many, to avoid hurting too much those that lose. The latter could be compensated, though.

Gabriel Felbermayr and Wilhelm Kohler argue that this cannot work for immigration. It works for international trade, because one can discriminate more easily against those who benefit the most from open borders, and they are willing to pay for the greater benefits from gains from trade. In the case of immigration, other considerations come into play, such as that one should not discriminate people by their origin. Thus it becomes impossible to tax some of their welfare gain from migration to compensate local losers. That is a problem of political feasibility, but that should not hinder us from advocating what is politically not feasible, because it is better than the politically feasible.