We have used ab initio density functional theory together with ab initio atomistic thermodynamics, and in situ x-ray absorption near edge spectroscopy (XANES) experiments, to study the oxidation of sub-nanometer clusters of Cu n O x supported on a hydroxylated amorphous alumina substrate in an O2-rich environment. We obtain (p , T) phase diagrams: these differ notably for the nanoclusters compared to the bulk. Both the theory and experiment suggest that in the presence of oxygen, the cluster will oxidize from its elemental state to the oxidized state as the temperature decreases. We obtain a clear trend for the transition of Cu n → Cu n O n/2: we see that the smaller the cluster, the greater is the tendency toward oxidation. However, we do not see a monotonic size-dependent trend for the transition of Cu n O n/2 → Cu n O n . We suggest that theoretically computed Bader charges constitute a simple yet quantitative way to align experimental measures of XANES edges with theoretical calculations, so as to yield oxidation states for nanoclusters. Our results have important implications for the use of small clusters in fields such as nanocatalysis and nanomedicine.