Practical methods to clean ITER's diagnostic mirrors will be essential to ITER's plasma operations. We report on laser cleaning of candidate ITER single-crystal molybdenum mirrors that were plasma coated with either carbon or beryllium films 150 to 420 nm thick. A pulsed Nd laser beam was focused to 1 to 2 J/cm2 and scanned at various speeds across the surface of a mirror. The cleaning effect was measured with a novel method that combined microscopic imaging and reflectivity measurements in the red, green, and blue spectral regions and at the H-alpha and H-beta wavelengths. No damage of the molybdenum mirror substrates was observed at the range of laser intensities used. For carbon-coated mirrors, complete removal of the film and restoration of the reflectivity were measured in some conditions. For the beryllium-coated mirrors, restoration of reflectivity has so far been incomplete. Heat transfer calculations suggest a shorter, [approximately]5-ns laser pulse would be optimal.