For modeling convective flows over a sphere or within a spherical shell, pseudospectral (PS) methods are in general far more cost-effective than finite difference- (or finite element) methods. This study confirms this, and proceeds by comparing a Fourier-PS implementation (based on a longitude-latitude grid) with one using spherical harmonics. For similar resolutions, these are found to be of similar accuracy. However, the former is computationally about ten times faster. ¿ 1997 American Geophysical Union