The efficient activation of methane and simultaneous water dissociation are crucial in many catalytic reactions on oxide-supported transition metal catalysts. On very low-loaded Ni/CeO₂ surfaces, methane easily fully decomposes, CH₄ -> C + 4H, and water dissociates, H₂O -> OH + H. However, in important reactions such as the direct oxidation of methane to methanol (MTM), where complex interplay exists between reactants (CH₄, O₂), it is desirable to avoid the complete dehydrogenation of methane to carbon. Remarkably, the barrier for the activation of C-H bonds in CHx (x= 1-3) species on Ni/CeO₂ surfaces can be manipulated by adding Cu, forming bimetallic NiCu clusters, whereas the ease for cleavage of O-H bonds in water, is not affected by ensemble effects, as obtained from density functional theory-based calculations. CH4 activation occurs only on Ni sites and H₂O activation on both Ni and Cu sites. The MTM reaction pathway for the example of the Ni₃Cu₁/CeO₂ model catalyst predict higher selectivity and a lower activation barrier for methanol production, compared with that for Ni₄-CeO₂. These findings point toward a possible strategy to design active and stable catalysts which can be employed for methane activation and conversions.