The laser-damage thresholds of single material and nanolaminate thin films were compared under continuous-wave (CW) illumination conditions. Nanolaminate films consist of uniform material interrupted by the periodic insertion of one or more atomic layers of an alternative material. Hafnia and titania were used as the base materials, and the films were deposited using atomic-layer deposition. The nanolaminates were less polycrystalline than the uniform films, as quantified using x-ray diffraction. It was found that the nanolaminate films had reduced laser-damage thresholds on smooth and patterned substrates as compared to uniform single-material films. This behavior is unusual as prior art indicates that amorphous (less polycrystalline) materials have higher laser-damage thresholds under short-pulse excitation. It is speculated that this may indicate that local thermal conduction affects breakdown more strongly under CW excitation than the dielectric properties that are important for short-pulse excitation.