In computed tomography (CT), the representation of edges between objects of different densities is influenced by the limited spatial resolution of the scanner. This results in the misrepresentation of density of narrow objects, leading to errors of up to 70% and more. Our interest is in the imaging and measurement of narrow bone structures, and the issues are the same for imaging with clinical CT scanners, peripheral quantitative CT scanners or micro CT scanners. Mathematical models, phantoms and tests with patient data led to the following procedures: (i) extract density profiles at one-degree increments from the CT images at right angles to the bone boundary; (ii) consider the outer and inner edge of each profile separately due to different adjacent soft tissues; (iii) measure the width of each profile based on a threshold at fixed percentage of the difference between the soft-tissue value and a first approximated bone value; (iv) correct the underlying material density of bone for each profile based on the measured width with the help of the density-versus-width curve obtained from computer simulations and phantom measurements. This latter curve is specific to a certain scanner and is not dependent on the densities of the tissues within the range seen in patients. This procedure allows the calculation of the material density of bone. Based on phantom measurements, we estimate the density error to be below 2% relative to the density of normal bone and the bone-width error about one tenth of a pixel size.