The potentials of incoherent X ray scattering Compton tomography are investigated. Imaging materials of very different density or atomic number at once is a perpetual challenge for X ray tomography or radiography, in general. In a basic laboratory set up for simultaneous perpendicular Compton scattering and direct beam attenuation tomographic scans are conducted by single channel photon counting. This results in asymmetric distortions of the projection profiles of the scattering CT data set. In a first approach corrections of Compton scattering data by taking advantage of rotational symmetry yield tomograms without major geometric artefacts. A cylindrical sample composed of PE, PA, PVC, glass and wood demonstrates similar Compton contrast for all the substances, while the conventional absorption tomogram only reveals the two high order materials. Comparison to neutron tomography reveals astonishing similarities except for the glass component without hydrogen . Therefore, Compton CT bears the potential to replace neutron tomography, which requires much more efforts