In a previous paper by Zeppenfeld et al. [Phys. Rev. B 50, 14 667 (1994)] the dynamics of a Xe monolayer on Cu(110) was determined using inelastic He-atom scattering. Energy losses:at around 3.7 meV were assigned to a longitudinally polarized phonon localized in the Xe adlayer. The value of 3.7 meV was found to be in good agreement with the predictions derived using the corresponding Xe-Xe gas-phase potential. Since recently for Xe adsorbed on the two other low-index Cu single-crystal surfaces, Cu(100) and Cu(111), rather different results were obtained revealing a pronounced anomaly in the interaction between adsorbed Xe atoms, we have reinvestigated the Xe/Cu(110) system. Our new data demonstrates that the mode at 3.7 meV is not an inherent feature of the Xe adlayer and is most likely related to the presence of contaminations. Ail together the new data indicates that the anomaly in the interaction between the adsorbed Xe atoms is present for Xe adlayers on all Cu surfaces with low Miller indices, Cu(111), Cu(100), and Cu(110).