An extended version of the cascade-exciton model (CEM) of nuclear reactions is applied to analyze nucleon-induced fission cross sections for 209Bi and 208Pb nuclei in the 45- to 500-MeV energy range. The available data on linear momentum transfer are analyzed as well. The results are compared with analytical approximations resulting from a comparative critical analysis of all available experimental data. Systematic discrepancies between calculations and experimental data are revealed. A modification of the CEM is proposed, which significantly improves the model predictions for projectile energies above 100 MeV.