We have extended photon correlation spectroscopy down to a one-nanosecond time scale, and applied it to a study of layer undulations in freestanding smectic-A films of two cyanobiphenyl liquid crystals. Temporal correlations in the intensity of scattered light reveal an interesting combination of under- and overdamped modes. The underdamped mode is accurately described by a recently calculated correlation function of the smectic layer displacement, although its frequency and damping rate exhibit stronger dispersion at large optical wave vectors than expected from current dynamical models for smectic films.