DIRA-3D is an iterative model-based reconstruction method for dual-energy helical CT whose goal is to determine the material composition of the patient from accurate linear attenuation coefficients (LACs). Possible applications are, for example, to aid in calculations of radiation transport and dose calculations in brachytherapy with low energy photons, and in proton therapy. There was a need to replace the current image reconstruction method, the PI-method, with a weighted filtered backprojection (wFBP) algorithm for image reconstruction, since wFBP is used for image reconstruction in Siemens's CT-scanners. The new DIRA-3D algorithm implemented the program take for cone-beam projection generation and the FreeCT wFBP algorithm for image reconstruction. Experiments showed that the accuracies of the resulting LACs for the DIRA-3D algorithm using wFBP for image reconstruction were comparable to the one using the PI-method for image reconstruction. The relative LAC errors reached a value below 0.2% after 10 iterations.