A number of different methods for post reconstruction bone beam hardening (BBH) correction are available for conventional FBP reconstruction and are used in commercially available products. An incorporation of these existing methods into statistical iterative reconstruction for CT is desired for several reasons. There are two ways imaginable to incorporate the BBH correction into iterative reconstruction:The first option is to use the beam hardening corrected projectionsas input for the statistical iterative reconstruction. For this ithas to be considered that the noise level in the projection data changes due to the correction. The second option is to incorporate theinverse of the beam hardening correction into the forward projectionof the cost function, and derive an update equation from this modified cost function. Both methods are implemented and compared based on simulated data with respect to artifact suppression, image noise,and speed of convergence.