While accepting that an inverse relation of some kind exists between inequality and mobility, we begin by reviewing criticisms of recent attempts by economists to express this relation in terms of income inequality and mobility – the ‘Great Gatsby Curve’. This appears to be neither empirically secure nor theoretically well-grounded. Using a newly constructed European dataset, we then aim to show that if mobility is treated in terms of social class, rather than income, an inverse relation with social inequality can be suggested that is more complex but that has a stronger empirical and a more coherent theoretical basis. Our results indicate that European countries are best seen not as displaying entirely continuous variation in their relative rates of class mobility, but rather as falling into a number of comparatively high and low fluidity groups. We offer an interpretation of these results that starts out from the proposition that within societies with a capitalist market economy, a nuclear family system and a liberal democratic polity, some limit exists to the extent to which relative mobility rates can be brought towards equality. Variation in such rates can then be understood in terms of how close nations are to this limit, and whether they are moving towards or receding from it, but with different forms of inequality impacting on their fluidity trajectories in differing ways.