||Interpretation of films or coatings hardness measurements is difficult when the applied load transfers a part of the indentation energy to the substrate. For these conditions, in effect, the hardness value, which is obtained by measuring the indentation diagonal, represents a « composite » hardness. In a recent paper, Iost and Bigot  proposed a critical review of some models presented in the literature. In particular these authors recommend to use the Jönsson and Hogmarks model . Applied directly to thick coatings, this model does not bring accurate predictions. This is the reason why we have already proposed to modify this model [3, 4]. In this paper we give some supplementary elements in order to avoid any misunderstanding of the modification of Jönsson and Hogmarks model.