The structures of small Pd-Au clusters adsorbed on stepped MgO(100) are studied by Density-Functional Theory calculations, in the size range from 2 to 7 atoms for all compositions. A series of different structural motifs is singled out. These motifs are often in close energetic competition. It is shown that the adsorption in the vicinity of a step has strong effects on the preferential morphologies of these clusters. The driving forces for the stabilization of the lowest-energy structures are discussed. (C) 2013 Elsevier B.V. All rights reserved.