Recent experiments show that on rather thick Co films deposition of Cu or adsorption of CO or C can switch the magnetization direction along the surface normal. We present semi-empirical self-consistent tight-binding calculations for a semi-infinite hcp Co(0001) crystal. It appears that the contribution of the magnetic anisotropy-energy from the surface layer favors the in-plane alignment of magnetic moments. Various surface perturbations (Cu deposition or CO adsorption, artificial suppression of surface magnetization), however, reduce this contribution considerably or even change the sign of the electronic part of the magnetic anisotropy energy, thus making conditions for perpendicular magnetization more favourable.