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We study the issue of income convergence across countries and regions with a Bayesian model which allows us to use information in an efficient and flexible way. We argue that the very slow convergence rates to a common level of per-capita income found, for example, by Barro and Sala-i-Martin, is due to a'fixed effect bias' that their cross-sectional analysis introduces in the results. Our approach permits the estimation of different convergence rates to different steady states for each cross-sectional unit. When this diversity is allowed, we find that convergence of each unit to (its own) steady-state income level is much faster than previously estimated, but that cross-sectional differences persist: inequalities will only be reduced by a small amount by the passage of time. The cross-country distribution of the steady state is largely explained by the cross-sectional distribution of initial conditions.