We have studied the structure of small doubly charged carbon clusters using density functional (DFT) and coupled-cluster (CC) theories. We have found that, with the exception of C-4(2+) and C-7(2+), the most stable geometry corresponds to linear structures of D-infinityh symmetry. This is at variance with the behavior observed in neutral and singly charged carbon clusters. We have also evaluated dissociation energies corresponding to various dissociation channels that are useful in mass spectrometry experiments. This requires that absolute energies of neutral and singly charged species are evaluated at the same level of theory. As a byproduct of the latter calculations, we have evaluated first and second ionization potentials that are still unavailable in the literature. Harmonic frequencies for the doubly charged species have been also evaluated.