Simple, shallow-water models have been successful in reproducing two key observables in the atmospheres of the giant planets: the formation of robust, and fully turbulent, latitudinal jets and the decrease of the zonal wind amplitude with latitude. However, they have to date consistently failed in reproducing the strong prograde (superrotating) equatorial winds that are often observed on such planets. In this paper we show that shallow water models not only can give rise to superrotating winds, but can do so very robustly, provided that the physical process of large-scale energy dissipation by radiative relaxation is taken into account. When energy is removed by linear friction, equatorial superrotation does not develop; when energy is removed by radiative relaxation, superrotation develops at apparently any deformation radius.