A systematic structuring of magnetic fields over scales much smaller than the mean free path of photospheric photons may be responsible for the observed asymmetrical Stokes profiles. We explore this possibility by deriving the radiative transfer equation for microstructured magnetic atmospheres (the MISMA approximation). This equation is subsequently employed to show that very schematic MISMA scenarios for the penumbrae of sunspots, plage and network regions, and internetwork regions produce Stokes profiles that have the observed asymmetries. The details of these model atmospheres are of secondary importance, but the ease of generating the type of observed asymmetries with MISMAs is significant, so the existence of MISMAs deserves serious consideration. Should such microstructures exist, the techniques currently employed to infer properties of the solar photosphere need to be revised. MISMAs are also of concern for the physics of the photosphere itself. These two topics are briefly discussed.