The effect of adsorbed oxygen on the LEED fine structure features of Cu(001), Cu(110) and Cu(111) is investigated. The adsorption process is followed by AES and CPD measurements. Changes in the relative intensity of the fine structure features are related to changes in the surface order and smoothness. It is empirically established that a rough surface produces relatively weak fine structure features compared with a similar smooth surface. This is attributed to a reduction in reflectivity of the surface potential barrier. It is also shown empirically that increasing disorder on the crystal surface leads to a preferential damping of the fine structure close to the emergence. This effect is seen in the change of the relative intensity of the fine structure features during the adsorption of oxygen. Observations of these features are used to test several models proposed for the oxygen adsorption sites on these surfaces.