Total cross sections for proton- and deuteron-induced-fission of 208Pb and 238U have been determined in the energy range between 500 MeV and 1 GeV. The experiment has been performed in inverse kinematics at GSI Darmstadt, facilitating the counting of the projectiles and the identification of the reaction products. High precision between 5 and 7 percent has been achieved by individually counting the beam particles and by registering both fission fragments in coincidence with high efficiency and full Z resolution. Fission was clearly distinguished from other reaction channels. The results were found to deviate by up to 30 percent from Prokofievs systematics on total fission cross sections. There is good agreement with an elaborate experiment performed in direct kinematics.