Williamson (1965) argued that catching up countries experiencing strong national growth tend also to see a widening in regional disparities, whereas in more developed economies strong national growth and falling regional disparities could go hand in hand. We find some evidence of a trade-off between national growth and regional dispersion in the EU's Cohesion countries, notably in Spain and Ireland. We also find some evidence of spread effects in some richer EU Member States, although no inevitable link between lower regional disparities and stronger national growth. The potential policy implications of this analysis are also examined.