This paper shows that if the off-beam idle detectors in the detection ring of a fourth-generation x-ray computed tomography (CT) system are used to measure the scattered radiation, it is numerically feasible to reconstruct electron-density images to supplement the conventional attenuation-coefficient images of transmitted radiation. It is also shown that by combining these two images, composition changes can be detected with the aid of an effective-atomic-number indicator. The required image-reconstruction algorithms are developed and tested against Monte Carlo simulated measurements, for a variety of phantom configurations. In spite of the relatively poor statistical quality of scattering measurements, it is demonstrated that electron-density images of reasonable quality can be obtained. In addition, it is shown that composition discrimination is possible for materials of effective atomic number greater than five, in the photon energy range of a typical medical x-ray CT system operating at 102 kV_p. The obtained supplementary electron-density and composition images can be useful in radiotherapy planning and for studying tumour histology, as well as in industrial and security applications where identification of materials based on density and composition is important.