A simple model potential is proposed to describe the interaction of a valence electron with the alkali core, which incorporates the correct asymptotic behavior in terms of dipolar polarizabilities, and the short-range exchange effects in terms of a hard core adjusted to give the correct energy for the valence electron. Based on this potential, simple wave functions are developed to describe the (H-alkali)(+) and (alkali-alkali)(+) ions. These wave functions exhibit some important structures of the ions, and provide a universal description of the properties of all (H-alkali)(+) and (alkali-alkali)(+) ions, in particular, the equilibrium separations of the nuclei and the corresponding dissociation energies. They also allow us to calculate the dipolar polarizabilities of Li-2(+), Na-2(+), K-2(+), Rb-2(+), and Cs-2(+).