The Bayesian method was applied to the simultaneous fitting of neutron transmission measurements on five thin and two thick samples of 240Pu to obtain the parameters of the very large resonance near 1 eV. The results of the analysis are E0 = 1.0564 ± 0.0006 Γγ, = 30.3 ± 0.3 meV, and Γn = 2.45 ± 0.02 meV. Some evidence in the data of a small deviation from the usual “weak binding” model for Doppler broadening of the theoretical resonance shape is presented. Transmission measurements on samples of 235U, 239Pu, and 240Pu also were made over the thermal energy region and their neutron total cross sections were derived. Fits of the form A + B to the cross-section data in the interval from 0.02 to 0.03 eV resulted in the values 690 ± 5, 1025 ± 6, and 284 ± 2 b for the 2200 m/s total cross sections of 235U, 239Pu, and 240Pu, respectively.