Total neutron cross sections of the heavy and actinide nuclei 181Ta, 197Au, 232Th, 233U, 235U, 238U, 239Pu, and 240Pu were measured from 30 keV to 4.8 MeV. The experimental procedures emphasized a high consistency of the measured data. Systematic uncertainties, excluding those associated with sample masses, were ≲0.5% and statistical uncertainties were typically (1.0 to 2.0)%. At low energies attention was given to resonance self-shielding effects. Experimental confirmation for theoretical calculations of the latter was sought by measuring with samples of different thicknesses for two of the nuclei. The measured total cross sections were interpreted in terms of a spherical optical model and a deformed coupled-channels model.