The invention relates to a method for combined bone hardening and scattered radiation correction in X-ray computed tomography of a heterogeneous object with a CT system comprising an X-ray source moved around an object, a flat detector with a large number of distributed detector elements which detect measuring beams from a focal point of the X-ray tube, and a control and arithmetic-logic unit—by iterative reconstruction and segmented vectorial reprojection calculation, wherein a scattered radiation correction and a radiation hardening correction are carried out in each iteration cycle for at least two different material components of the object being examined. The invention also relates to an X-ray CT system for carrying out this method.