The global demand for air travel and air transport is expected to further increase in the next couple of years, and so the environmental protection will also increasingly come into focus again. In the aviation sector, this means not only saving fuel and reducing emissions but also reducing the noise pollution caused by aircrafts. For this purpose, sound-absorbing acoustic liners are used, which consist of a sandwich structure with one perforated skin layer. To reduce weight, these outer layers are often made of carbon fiber-reinforced plastic (CFRP). For manufacturing these CFRP skin layers, laser drilling offers specific benefits, but when it comes to industrial applications, further process improvements are necessary. Although laser microdrilling is a well-known process in laser materials’ processing, it has not yet been sufficiently investigated for the processing of carbon fiber-reinforced plastics. This study investigates the quality and efficiency of laser microdrilling with a 1.5 kW nanosecond-pulsed high-power laser for percussion drilling and helical drilling of thin CFRP laminates. The efficiency was evaluated in terms of drilling depth, the amount of energy required to remove a specific volume of material, and the time required to remove a specific volume of the material. The quality evaluation focused on the heat-affected zone and the hole taper. The efficiency and quality results were set in relation to higher-level parameters such as energy fluence in the laser spot, pulse overlap, or total energy applied. This facilitates future transferability to similar laser processes that may use laser machines and system technology with deviating specifications.