In a post-Brexit world, the U.K. might be pursuing an impossible trinity: Independence from the European Union, free trade, and less immigration. Data published by the Organization for Economic Co-operation and Development show that in services trade, which accounts for more than two thirds of U.K. value-added exports, the country already has fewer barriers than most rich countries in most sectors. If officials want to position the country as a beacon of free trade in a protectionist world, then there is one — rather awkward — area where reform could give the U.K. an edge: the ease with which foreigners can move to and work there. Even with the current free-movement stipulations which come as being part of the EU, there are still restrictions on non-nationals’ entry to certain professions.  The OECD figures show that in services sectors including accounting, architecture, legal, and tech, the biggest impediment to free trade are domestic rules that put obstacles like local-qualification requirements on people moving to Britain, even for a limited time, to work in these fields. For EU nationals, while they can — still — immigrate easily, the job of choice may be closed to them. For non-EU nationals, getting past border control without domestic qualifications may be impossible.  “In professional services, general measures on the temporary movement of workers contribute significantly to the index because of the prominent importance of the movement of people for trade in these sectors,” the OECD says in its report from February. While the regulatory environment is “favorable,” limitations on the temporary movement of people “affect services providers in all sectors,” it says. While it might be sensible to have local requirements, particularly with the U.K.’s common-law legal system, the country is far from the most open in this respect even in Europe. For example, Ireland, Germany and Luxembourg all have less restrictive rules for the movement of people in the accountancy sector. So there would be a way to boost competitiveness on a global scale in services trade, but it’s just not one that politicians seeking to curb immigration might find easy to digest. That’s among the many uncomfortable truths that, according to Malcolm Barr, an economist at J.P. Morgan Chase Bank in London, Britain will have to face in the post-EU environment. “Some claim that the body of EU regulation weighs U.K. businesses down with “too much red tape,” he said. “Any belief that freeing U.K. businesses from the weight of such regulation is going to generate a boost to U.K. economic performance is, in our view, mistaken.”