We propose a method for designing a one-dimensional random perfectly conducting surface which, when illuminated normally by an s-polarized plane wave, scatters it with a prescribed angular distribution of intensity. The method is applied to the design of a surface that scatters light uniformly within a specified range of scattering angles, and produces no scattering outside this range; a surface that acts as a Lambertian diffuser; and a surface that suppresses single-scattering within a specified range of scattering angles. This method is tested by computer simulations, and a procedure for fabricating such surfaces on photoresist is described.