Total photofission cross sections for 238U, 235U, 233U, 237Np, 232Th, and natPb have been measured simultaneously, using tagged photons in the energy range Egamma=0.17-3.84 GeV. This was the first experiment performed using the Photon Tagging Facility in Hall B at Jefferson Lab. Our results show that the photofission cross section for 238U relative to that for 237Np is about 80% over the entire energy range, implying the presence of important processes which compete with fission. If we assume that for 237Np the photofission probability is equal to unity, we observe a significant shadowing effect, starting below 1.5 GeV.