The state-of-the-art ab initio calculations are performed to study surface states on stepped Cu(111) surfaces with the terrace widths ranging from 12 to 21 Å. In agreement with experiments of Hansmann et al. [Phys. Review B 67, 121409(R) (2003)], close to the Fermi energy we reveal electronic states significantly affected by repulsive potential at steps. Our calculations demonstrate that the position of such states is strongly dependent on the terrace width. By using the Kronig-Penney model and ab initio results, the strength of potential barriers at step edges is determined. It is shown that the strength of the confining barriers on Cu(111) vicinals can be significantly affected by decoration of step edges with monatomic Fe wires, similar to recent experimental findings of Shiraki et al. [Phys. Rev. Lett. 92, 096102(2004)]. Spin-dependent scattering of surface electrons at Fe wires is shown to result in the formation of spin-polarized surface states on stepped Cu(111) surfaces. The majority states remain unaffected. A localization of the minority states at Fe wires suppresses the confinement-like features of the local density of states.