Computations of mode-scattering coefficients arising from ionospheric perturbations at sunrise and sunset lines are reported in the paper. The computations are based on an analysis that exploits the concept that radio waves at low frequencies propagate in a nonuniform, spherical, ‘Earth-ionosphere waveguide’ with finite, surface-impedance boundaries. The computed data are compared with available experimental data at 18kHz for both day-night and night-day propagation paths. The computed data for v.l.f. radio frequencies indicate that, for an ionospheric effective-height change of 20km, the magnitudes of the first-second and second-first mode-conversion coefficients pass through minima about 16kHz provided that the length of the transition region is less than 800km.