We have examined strain-relaxation of Co-2 x 2 islands grown on the Ag/Ge(111)root 3 x root 3 surface by analyzing scanning tunneling microscopy images. We have found that the Co-2 x 2 islands commonly adopt a more compact arrangement as compared to that of the Ge(111) substrate, however they differ in a degree of an atomic compactness. We have not found a distinct relation between strain-relaxation and the island height. Three groups of islands have been identified upon analyzing a correspondence between strain-relaxation and the island size: (i) small islands (not bigger than 80 nm(2)) with a high atomic compactness, displaying fixed inter-row distances, (ii) small islands with unfixed distances between atomic rows, and (iii) big islands (bigger than 80 nm(2)) with fixed inter-row distances. but with a less compact atomic arrangement compared to that of the first two groups. We propose a model to account for the relation between the relaxation and the island size. (C) 2012 Elsevier B.V. All rights reserved.