A cooling scheme for trapped atoms is proposed, which combines cavity-enhanced scattering and electromagnetically induced transparency. The cooling dynamics exploits a three-photon resonance, which combines laser and cavity excitations. It is shown that relatively fast ground-state cooling can be achieved in the Lamb-Dicke regime and for large cooperativity. Efficient ground-state cooling is found for parameters of ongoing experiments. © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft.