We have recently proposed and investigated a planar imaging method called multiple-image radiography (MIR) that concurrently produces three two-dimensional images that reveal information about the ultra-small-angle scattering and refractive index properties of the object, in addition to an almost scatter-free radiographic image that depicts the projected absorption properties of the object. In this work, we develop and implement experimentally a computed tomography (CT) version of MIR, referred to as multiple-image CT (MICT), that produces three volumetric images of these object properties. The appropriateness of a linear imaging model is validated experimentally by use of phantom studies. The MICT method is employed for reconstruction of images of two biological phantoms using measurement data produced by a synchrotron light source.