Using a quasi-ab initio molecular-dynamics method we have studied two-dimensional (2D) versus three-dimensional (3D) structures in Co clusters deposited on Cu(001) finding that the magnetism plays a relevant role. For the magnetic Co₂₅ supported cluster, the influence of such a 2D to 3D structural change on the magnetic properties (magnetic-moment distribution an average magnetization) is investigated through self-consistent calculations within a spd tight-binding model parametrized to ab initio results for the ideal Co monolayer on Cu(001).