Biomechanical theories to predict bone remodelling have used either mechanical strain or microdamage as the stimulus driving cellular responses. Even though experimental data have implicated both stimuli in bone cell regulation, a mechano-regulatory system incorporating both stimuli has not yet been proposed. In this paper, we test the hypothesis that bone remodelling may be regulated by signals due to both strain and microdamage. Four mechano-regulation algorithms are studied where the stimulus is: strain, damage, combined strain/damage, and either strain or damage with damage-adaptive remodelling prioritised when damage is above a critical level. Each algorithm is implemented with both bone lining cell (surface) sensors and osteocyte cell (internal) sensors. Each algorithm is applied to prediction of a bone multicellular unit (BMU) remodelling on the surface of a bone trabecula. It is predicted that a regulatory system capable of responding to changes in either strain or microdamage but which prioritises removal of damaged bone when damage is above a critical level, is the only one that provides a plausible prediction of BMU behaviour. A mechanism for this may be that, below a certain damage threshold, osteocyte processes can sense changes in strain and fluid flow but above the threshold damage interferes with the signalling mechanism, or causes osteocyte apoptosis so that a remodelling response occurs to remove the dead osteocytes.