The small-scale motions of a liquid surface due to capillary waves are found to be dominated by over-damped, local modes of oscillation. For values of the wave vector k in the under-damped regime, where viscosity is relatively unimportant, the long-range part of a local mode can excite the normal modes that are the usual focus of capillary-wave theory. The calculated surface roughness at high k values is larger than is given by normal mode treatments, so is in better agreement with the results of recent studies of the scattering of synchrotron radiation from liquid interfaces.