We study the problem of two Kondo impurities in a small system. Using a slave boson approach we investigate the effect on the electron confinement of the Kondo physics of the two impurity problem. We show that the confinement splits the symmetric and antisymmetric channels and for small systems weakly coupled to a reservoir this gives two well defined behaviors: For the Fermi energy lying at a resonant state, the two impurities are Kondo screened with two characteristic energy scales. For the Fermi energy between two resonances, the inter-impurity interaction destroys the Kondo effect.