The scattering of high-frequency (HF) electromagnetic radiation from slightly rough, good conducting surfaces is presented. The analysis is based on a decomposition of the relevant space using generalized functions. The fundamental analysis incorporates a general source and involves all scattering orders for the normal component of the field. Subsequently, derivation of the scattered electric field (to third order in scatter) using a pulsed dipole source is effected. The first 2 orders are used to deduce an estimate of radar cross sections of bounded regions or targets when operation is carried out in the backscatter mode. Conditions of small height and small slope are imposed. Application is made to the determination of the first-order cross section of a perfectly conducting sphere (within the limits of the imposed constraints) and of an exponential boss. The results are shown to be consistent with Rayleigh scattering theory. ¿ 2000 American Geophysical Union