There has been some controversy regarding the Scanning tunneling microscopy (STM) spectra of Co overlayers on Cu(1 1 1). Recent experiments [Phys. Rev. Lett. 90 (2003) 236801; Phys. Rev. Lett. 92 (2004) 57202] find a peak 0.4 eV below the Fermi energy, at the onset energy of the Cu(1 1 1) surface state, while the previous work [Phys. Rev. Lett. 85 (2000) 4365] found two peaks, one 1 eV below the Fermi level and the other 0.5 eV above it. To address this problem we have performed both ab initio and parameterized tight-binding calculations for a Cu(1 1 1) slab coated with Co layers. The parameterized calculations allow larger unit cells and a better representation of the spill over region. The basis set used contains s, p and d orbitals and also extra s orbitals near the surface for the spill over. Our results for the local density of states at the site of the extra s orbital and at the Co surface site reproduce the feature at -0.4 eV, which also appears in pure Co slabs, and which is, therefore, not related to the Cu(1 1 1) surface state.