The fission cross-section ratios 241Am: 235U and 243Am: 235U were measured as a function of neutron energy from 0.2 to 30 MeV using ionization fission chambers, the threshold cross-section method, and the time-of-flight technique at the Lawrence Livermore National Laboratory 100-MeV electron linear accelerator. Our experimental procedure required accurate measurements of the isotopic composition of fissionable material within fission chambers containing a mixture of the threshold isotope (i.e., 241Am or 243Am) and 235U. The measured cross-section ratios, averaged over the neutron energy interval from 1.75 to 4.00 MeV, were 1.648 ± 0.046 and 1.391 ± 0.039, respectively.