Advances in diagnosis and treatment of some bone disorders can be made by understanding the linkage between mineral content and mechanical function. Bone is approximately half by volume a hydrated protein network, and the remainder is a biomineral analogue of hydroxyapatite. In the current work, paired measurements of mechanical properties, using nanoindentation, and of bone mineral volume fraction, computed from quantitative back-scattered electron imaging, were made on six different types of normal and outlier bone samples. Local elastic modulus was plotted against mineral fraction and compared with predictions of engineering bounds for a two-phase composite material. Experimental data spanning the composite bounds showed no one-to-one relationship between mechanical stiffness and bone composition, excluding the possibility of any single, simple composites model for bone at nanometer length-scales.