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The structure of low-mass stars irradiated by a close companion is considered. Irradiation modifies the surface boundary conditions and thereby also the adiabatic constants of their outer convection zones. This then changes the models' radii and luminosities. For short-period M dwarf binaries with components of similar mass, the radius inflation due to their mutual irradiation is found to be < 0.4%. This is an order of magnitude too small to explain the anomalous radii found for such binaries. Although stronger irradiation of an M dwarf results in a monotonically increasing radius, a saturation effect limits the inflation to < 5%.