In this paper we develop a two-scale model of sea-surface roughness, in which for the first time the randomness of both long and short waves is taken fully into account. The model includes long-wave-short-wave interactions, dissipation of the short-wave energy by breaking, and regeneration by the wind. This leads to an integral equation for the short-wave steepness, which is solved by iteration. The effects of wind speed and of long-wave steepness upon the distribution of roughness at the long-wave crests are calculated and discussed. Also the effect of a band-width parameter for the long-wave spectrum. A random noise source can be included.