We present a method for numerically generating a one-dimensional random surface, defined by the equation $x_3 = zeta(x_1)$, that suppresses single-scattering processes in the scattering of light from the surface within a specified range of scattering angles. Rigorous numerical calculations of the scattering of light from surfaces generated by this approach show that the single-scattering contribution to the mean scattered intensity is indeed suppressed within that range of angles.