The Cu(4 1 0)-O surface, involving a 0.5 monolayer (ML) coverage of oxygen, is known to be extremely stable and a range of Cu(1 0 0) vicinal. surfaces facet to (4 1 0) in the presence of adsorbed oxygen. A new surface X-ray diffraction investigation of this surface has been conducted to determine its structure, and the detailed structural parameter values obtained are compared with the results of a density functional theory (DFT) calculation. The results show that the metal structure is unreconstructed, with the oxygen forming an overlayer with 0.25 ML O atoms at near-colinear step-edge sites and 0.25 NIL O atoms at mid-terrace hollow sites, approximately 0.6 Angstrom above the terraces. The large number of independent structural parameters potentially relevant to this vicinal surface presents a significant challenge for unique structural optimisation, but various missing row reconstruction models can be clearly excluded. Two detailed structural solutions are identified which give equally acceptable fits to the X-ray diffraction data after imposition of a Lennard-Jones penalty factor. These models differ especially in the O positions, but one is found to be more favoured by comparison with the results of the DFT calculations, and by considerations based on bond lengths and valence. Substantial relaxations from the bulk metal positions occur for the outermost Cu atoms; the ability of the vicinal surface to relax in this way may help to account for its stability compared with the missing row reconstruction induced by oxygen chemisorption on the Cu(1 0 0) surface. (C) 2002 Elsevier Science B.V. All rights reserved.