A version of the integral equation method is developed, which applies to scattering from a surface of a substance with a large dielectric constant ϵ. An impedance boundary condition for the tangential components of electric and magnetic fields on the scattering surface is used, and the integral equation for the tangential components of the total magnetic field on a surface is formulated. This equation is applied to the problem of electromagnetic scattering from a slightly rough surface. It is demonstrated that the commonly used perfect conductor approximation (PCA) (ϵ=∞) can adequately describe scattering in the case of extremely large &egr; only. The greatest sensitivity in scattering occurs when the incident and/or scattered waves are vertically polarized. For such cases the PCA does not work until ϵ>104. In the particular case of scattering from the ocean (|ϵ|~65), the PCA fails to provide an adequate description of the phenomena for either horizontally or vertically polarized waves, for practically all incidence and scattering angles. ¿ 1999 American Geophysical Union