Bone-mineral measurements using quantitative computed tomography (QCT) are commonly based on comparisons with solutions in water of known concentrations of K2HPO4. In this paper are described theoretical and experimental studies that have led to the conclusion that large systematic errors can arise in these measurements, depending on the soft-tissue and fat concentrations in the vertebral spongiosa. In the case of single energy scanning, such large errors have been identified to be due to the varying water content (displacement effect) in the calibration samples and the varying fat content in the region of interest (ROI) within the patient. In the case of dual energy scanning, the error arises because when normalized to that of water, the mass attenuation coefficient of fat increases with photon energy while the reverse is true for K2HPO4. Our studies have also revealed that total trabecular bone density (which includes the mineral, soft tissue, and fat) can be much more accurately determined by the dual energy QCT method than bone mineral alone. This finding is especially interesting since there have been several reports in the literature suggesting that bone density rather than bone-mineral content is a better predictor of the risk of osteoporosis-related fractures.