The structure and stability of small copper clusters with up to ten atoms has been determined both for the neutral and the ionic clusters with density functional calculations. The calculations were of all-electron type. The structure optimization and frequency analysis were performed on the local density approximation level with the exchange correlation functional by Vosko, Wilk, and Nusair. Subsequently improved calculations for the stability were based on the generalized gradient approximation, where the exchange correlation functional of Perdew and Wang was used. Finally, the binding energies, ionization potentials, electron affinities, and separation energies were calculated. The results show that the trends are in agreement with available experimental data.