The structure of the low-lying levels in the mirror nuclei 57 Ni and 57 Cu is described within the extended unified model. The problem of single-particle energies in 56 Ni is treated in detail. \"Bare\" single-particle energies are extracted from existing experimental data for the energy levels in 57 Ni and 57 Cu by carefully considering the influence of the coupling to excitations of the core. Important contributions arise, influencing especially the results on the spin-orbit splitting. The differences between the Coulomb energy shifts of various orbitals in 56 Ni are discussed and compared with those resulting from Hartree-Fock calculations carried out using a broad range of Skyrme interactions. The parameters of the Woods-Saxon potential reproducing these neutron \"bare\" single-particle energies and the charge root-mean-square radius of 56 Ni are extracted. It is demonstrated that the contributions associated with the Thomas-Ehrman effect and the electromagnetic spinorbit interaction are important and large enough to account for the differences between the Coulomb energy shifts of the single-particle levels in 56 Ni.