Polychromaticity of the X-rays used in computed tomography (CT) has made it difficult to establish an absolute scale for CT values and has made quantitative comparisons between patients unreliable. The spectral shift of the X-rays depends on the material distribution within the structure measured and is significant if substantial amounts of bone, fat, or injected contrast material are present. A material-selective beam hardening correction procedure has been developed that allows the reconstruction of good approximations of linear attenuation coefficients with respect to a reference energy. With the aid of mathematical simulations and measurements on a physical phantom, the feasibility of the procedure and its insensitivity with regard to energy settings and other machine parameters are documented.