We investigated when the reflectance R(p) for p-polarized light becomes exactly zero in an attenuated-total-reflection configuration where surface plasma waves at a metal–dielectric interface are excited. We particularly studied the reflection from coated metal mirrors at infrared wavelengths, where the complex refractive index n2 = n2′ + in2″ of the dielectric coating has a real part smaller than unity. When a certain relation between n2′ and n2″ is satisfied, the reflectance R(p) versus incidence angle has deep broad minima for a large range of coating thicknesses. Such mirrors would be efficient reflection polarizers and would have high hemispherical thermal emissivities.