International audienceAn annealing-driven transition from a chemically disordered A1-like structure to a chemically ordered L10-like phase has been revealed for size-selected CoPt clusters with diameters from 2 to 4 nm, from experiment to theory confrontation. For chemically ordered particles, atypical lattice-parameter ratios c/a are inferred. This ratio is found to be remarkably different depending on the approach used (c/a>1 from x-ray absorption at the Co K edge and c/a≃0.94 from the Pt dominated x-ray diffraction). A first-principles theoretical study accurately explains this astonishing feature and provides a detailed understanding of the element-specific local relaxations, which are crucial in these nanoalloys