It is shown that the lineshape asymmetry of the X-ray photoelectron spectra of the Pt(4f) and Pd(3d) core-levels in small metal clusters decreases with the size of the cluster. Such changes are related to the changes of the density of states of the valence electrons and the effective core-hole potential at the Fermi level. The decrease of the asymmetry leads to a shift of the line position toward a higher binding energy (about half of the observed shift) as governed by the first moment rule.