Although quarter-wave multilayer dielectric coatings (QW MLDCs) usually offer the highest reflectivity possible at a single wavelength, this may not be the case at grazing angles of incidence. For incident angles greater than the Brewster angle, the p polarization absorption can easily be several orders of magnitude higher than the s polarization absorption due to the destructive interference between the reflection from the superstrate - top layer interface and the rest of the coating. An analytic approach is developed for designing optimum reflectivity coatings at grazing angles of incidence, once the fraction of s and p polarized light is given. These coatings can give at least an order of magnitude reduction over QW MLDCs in total coating absorption, even for the case where less than 0.1% of the incident radiation is p polarized. The absorption of the designs found from the analytic results compare favorably with designs generated using numerical methods of non-linear optimization.