Using administrative data on the globally connected super-rich in the UK, we study the effect of a large tax reform on migration behaviour. Prior to 2017, offshore investment returns for ‘non-doms’ – individuals tax resident in the UK but with connections to other countries – were untaxed. Average offshore investment returns for these individuals exceeded £420,000; even without considering other types of income, this puts them in the top 0.2% of the population. A reform in 2017 brought long-stayers and UK-born non-doms into the standard tax system, reducing their effective net of average tax rate by between 8.8% and 13.0%. We find that migration responses were limited: our central estimate of the migration elasticity is 0.02, and across a range of specifications we can rule out elasticities larger than 0.5. Using reforms for the UK-born super-rich who were living abroad, we find that migration elasticities are limited even for recent arrivals, for whom our central estimate is 0.18. Assuming similar elasticities for all non-doms, abolition of the preferential regime would increase tax revenue collected from non-doms by £3.2bn (84%).