Candidate global minima are obtained for H 3O +⋯(H 2O) n clusters with n⩽20 using a basin-hopping algorithm and an empirical, polarizable model potential. We have reoptimized the lowest minima for each system using a more accurate model and find extensive reordering of the potential energy surfaces, especially for larger n. For both model potentials a distorted dodecahedron surrounding an H 2O molecule is the global minimum for n=20, in good agreement with experiment. The gap between the latter structure and the lowest minimum with H 3O + in the centre is about 10–20 kJ mol −1.