In this work we analyze CO binding on small neutral copper clusters, Cun (n = 1-9). Molecular structures and reactivity descriptors of copper clusters are computed and discussed. The results show that the condensed Fukui functions and the frontier molecular orbital theory are useful tools to predict the selectivity of CO adsorption on these small clusters. To get further insight into the CO binding to copper clusters, an energy decomposition analysis of the CO binding energy is performed. The Cs symmetry of the formed CunCO clusters (n = 1-8) allows the separation between the orbital interaction terms corresponding to donation and back-donation. It is found that, energetically, the donation is twice as important as back-donation.