We present and discuss measurements of electron-irradiation damage in polystyrene and other polymers, based on fading of the 7-eV energy-loss peak. These measurements suggest a large increase in characteristic dose as the electron-beam diameter is reduced from 1 μm to below 1 nm. This finding is discussed in terms of secondary-electron production and delocalization of the inelastic scattering, both as it affects the volume of specimen in which the energy is deposited and the volume giving rise to the inelastic signal used to assess the damage.