In many applications common in testing for convergence the number of cross-sectional units is large and the number of time periods are few. In these situations asymptotic tests based on an omnibus null hypothesis are characterised by a number of problems. In this paper we propose a multiple pairwise comparisons method based on an a recursive bootstrap to test for convergence with no prior information on the composition of convergence clubs. Monte Carlo simulations suggest that our bootstrap-based test performs well to correctly identify convergence clubs when compared with other similar tests that rely on asymptotic arguments. Across a potentially large number of regions, using both cross-country and regional data for the European Union, we find that the size distortion which afflicts standard tests and results in a bias towards finding less convergence, is ameliorated when we utilise our bootstrap test.