This work examines the extraction of mechanical properties from instrumented indentation P–h s curves via extensive three-dimensional finite element analyses for pyramidal tips in a wide range of solids under frictional and frictionless contact conditions. Since the topography of the imprint changes with the level of pile-up or sink-in, a relationship is identified between correction factor β in the elastic equation for the unloading indentation stage and the amount of surface deformation effects. It is shown that the presumption of a constant β significantly affects mechanical property extractions. Consequently, a new best-fit function is found for the correlation between penetration depth ratios h e /h max, h r /h max and n, circumventing the need for the assumption of a constant value for β, made in our prior investigation [Acta Mater. 53 (2005) pp. 3545–3561]. Simulations under frictional contact conditions provide sensible boundaries for the influence of friction on both h e /h max and h r /h max. Friction is essentially found to induce an overestimation in the inferred n. Instrumented indentation experiments are also performed in three archetypal metallic materials exhibiting distinctly different contact responses. Mechanical property extractions are finally demonstrated in each of these materials.