The problem of high-frequency diffraction by a smooth lossy body with high conductivity is considered. In addition to the geometrical optics approximation, additional asymptotic terms are derived to take into account the curvature of the boundary and material properties. Since these higher-order terms are derived by taking into account exact boundary conditions, it is easy to learn about the limitations of impedance conditions and to determine more accurate approximate conditions. The obtained higher-order boundary conditions and their limitations are numerically validated by solving Muller's second-kind integral equations. © 2014 IEEE.