Previously, we have investigated the possible role of osteocytes as mechano-sensors, and mediators of bone turnover. It was found that the proposed regulatory mechanism produced morphologies of trabecular bone, under particular loading conditions, which were consistent with morphogenesis and adaptation as seen in reality. The main objective of this study was to descern whether lining cells or osteoblasts could possibly play a similar role as effectively with regard to their capacity for self-optimization of the trabecular architecture, in terms of a low apparent mass to stiffness ratio. For that purpose the earlier analyses with osteocytes as mechano-sensors, distributed throughout the bone, were repeated for mechano-sensors located at bone surfaces only. Compared to the osteocyte model, the surface cell remodelling algorithm was reluctant to change its architecture, which implies that it is less sensitive to changes in the loading pattern. This resulted in less efficient bone adaptation, which was reflected by a considerably higher relative mass for a similar apparent stiffness in the loading direction. In other words, more mass is needed to obtain an equally stiff structure, at the apparent level, with respect to the externally applied loads. Furthermore, stresses and strains at the tissue level vary across a much wider range, relative to the osteocyte model, where the higher incidence of elevated strains indicates an increased failure risk. Therefore, we conclude that mechanical information at the bone surface may not be sufficient to adequately regulate functional bone adaptation.