By deposition in ultra-high vacuum of cobalt on a Ge(111)–c(2 × 8) surface, Mocking et al. obtained a surface reconstruction. In the present paper, we analyse the related atomic structure, proposed by these authors, by means of density functional theory calculations. The surface presents ordered clusters that consist of six Ge atoms arranged in a triangle, lying above three Co atoms. The latter are located at substitutional positions within the top plane of the Ge(111) first bilayer. These clusters are similar to what is obtained on part of the Co-induced Si(111) surface. For this surface, the clusters are terminated either by six Si atoms or by one, two or three adatoms above the six Si atoms. As the Co–Ge clusters systematically display six protrusions in the scanning tunnelling microscopy measurements by Mocking et al., we investigated why Ge adatoms are not present. Comparison of the Gibbs energy, interatomic distances, as well as charge density indicates that Ge adatoms on top of Co-Ge clusters are less stable than Si adatoms in the Co-Si system. Copyright © 2013 John Wiley & Sons, Ltd.