The cause of the fast zonal winds on the large gas planets is disputed. To investigate their possible origin by convection in the planets' molecular hydrogen layer, I study simple numerical models of thermal convection in a rotating sphere at low Ekman numbers for Rayleigh numbers up to 100 times critical. With stress-free boundaries and high Rayleigh number it is possible to reproduce the observed magnitudes of the zonal and non-zonal flow components at the surfaces of Jupiter and Saturn. While only three flow bands are found for a thick convecting shell, the number increases to seven for a shell with an inner-to-outer radius of 0.6. ¿ 2001 American Geophysical Union