A compilation of brightness temperature data in the millimetre and sub-miUimetre wavelength ranges is used to obtain an empirical relation Tn --6"2 ~ between brightness temperature and wavelength, valid between 1 mm and 1 cm. An analytically soluble model, giving electron temperatures and densities between 1500 km and 4000 km above the photosphere is derived from this relationship, and eclipse data of Thomas and Athay, of the emission at the head of the Balmer continuum. Although this over-simplified model lacks precision in the height co-ordinate, it allows a scale height of around 1000 km for electrons to be deduced, and supplies a convincing test for the absence of hydrostatic equilibrium throughout the region. A more comprehensive and reliable though still simplified numerical model is then presented, being a modification of previous models accounting only for millimetre data. It shows marked departure from UV derived models in this region, and an explanation for the discrepancy is proposed in terms of thermal inhomogeneities on the scale of the chromospheric supergranulation. The stratified model is then geometrically modified to account for observed centrelimb profiles of the Sun measured throughout the sub-millimetre and millimetre region. The scale of any roughness thus introduced is related to the notable lack of millimetric limb brightening, and observational tests for that scale are suggested here. A qualitative picture of this part of the chromosphere is proposed, consistent with existing observations in the millimetre, visible and UV regions of the spectrum.