A method that corrects for artifacts in X-ray transmission scanners created by the alteration of the energy spectrum by bone is described. The method involves two reconstructions of the pictures: the first establishes the approximate distribution of bone and the second enables the artifacts to be eliminated. The first reconstruction is needed to establish the total amount of bone along each ray. Assuming that the X-ray energy spectrum is known, it is shown how the line integrals can be corrected. The method was tested on several mathematical phantoms as well as on human head data. The nonlinear nature of the spectral artifacts is shown to produce streaks in certain phantoms.