The diffusion and maximum anisotropy approximations are compared in the calculation of the electron distribution function for steady-state polar optical scattering in III-V semiconductors. An expansion of the steady-state Boltzmann equation in powers of (EO/E) is made for a high electric field E where EOis the characteristic critical electric field. This expansion is a fairly good approximation for certain ternary III-V semiconductors. The electron distribution function found by the diffusion approximation is useful only as a functional; a modified maximum anisotropy approximation gives a valid electron distribution function.