The effects of sphericity and gravity upon Rayleigh-wave dispersion are examined. The widely used empirical correction of Bolt and Dorman (1961), although originally determined from a limited set of earth models, appears to predict phase-velocity curves in a spherical gravitating earth from flat earth calculations to almost 1 per cent accuracy, as claimed, for five earth models chosen to reproduce the considerable range of observed dispersion. Its application in the past therefore does not seem likely to have introduced large errors in inversion of such dispersion to determine earth structure. The use of spherical gravitating earth normal mode calculations in computing dispersion is strongly urged: for those without access to the computing facilities required by the complexity of the numerical problem a new empirical correction based on flat earth group velocity is proposed. This predicts Rayleigh-wave phase velocity dispersion in a spherical gravitating earth to better than 0.4 per cent in the period range 10 to 200 sec. Even better precision can be obtained by application of the tables of corrections given for different types of crustal and upper mantle structures.