CuO/CeO2 catalysts where the support has different nanoparticle shapes exposing different lattice planes are examined for the preferential oxidation of CO in the presence of excess H2 (CO-PROX reaction) in operando DRIFTS conditions. Even for catalysts with same surface concentration of Cu the selectivity for CO2 formation is found close to 100% up to higher temperatures when the support is in form of nanocubes (exposing the less stable (001) lattice planes). DRIFTS data allow relating this to a higher stability of the Cu species forming the Cu+ carbonyls associated to the high activity and selectivity, so that they are fully reduced at higher temperature in agreement with TPR data. DFT calculations show that CuO nanoparticles interact more strongly (distorting more their structure) with the CeO2 (001) surface than with the (111) surface, while XRD indicates that the formation of well developed CuO nanocrystals is more difficult on nanocube shaped CeO2 than on other CeO2 morphologies. Also EPR spectra show that the CuO entities nucleate on the ceria nanocubes differently. The higher stabilization of the oxidized state indicated by DFT, together with the mentioned structural distortion, may be then the reason for the improved selectivity.