We present a systematic study of the radial brightness profiles in H alpha of a set of H ii regions in 6 late-type spiral galaxies, complete down to stated limiting luminosities. We have sufficient linear resolution in our observations to be able to fit models in which the effects of the radial fall off in density and in mean degree of ionization can be distinguished. We find a sharp break in the plot of internal radial brightness gradient against luminosity at a luminosity in H alpha of 10(38.6) erg/s in all these objects. For lower luminosities the gradients are almost invariant, showing only a slight tendency to steepen with luminosity; at this critical value there is a jump to higher gradients, and at higher luminosities the gradients steepen progressively. This is consistent with the regions showing a transition from ionization-bounded to density-bounded behaviour, in conformity with evidence from H ii region luminosity functions presented in previous studies.