Long-range correlations, which are partially responsible for the observed fragmentation and depletion of low-lying single-particle strength, are studied in the Green's function formalism. The self-energy is expanded up to second order in the residual interaction. We compare two methods of implementing self-consistency in the solution of the Dyson equation beyond Hartree-Fock, for the case of the 16O nucleus. It is found that the energy-bin method and the BAGEL method lead to globally equivalent results. In both methods the final single-particle strength functions are characterized by exponential tails at energies far from the Fermi level.