Severe damages may occur during the drilling of carbon fiber reinforced plastics (CFRP). In practice, this damage is limited by adding a backup support to the drilled parts. For some aeronautical parts with curvatures, backing up parts is a demanding process. In order to simplify the operation, this research studies the effect of using a configurable setup to support parts on the resulting quality of drilled holes. The test coupons referenced in this study are twenty four-plies unidirectional laminates made of carbon fibers and epoxy resin. Different signals were measured during the drilling process for these laminates, including the thrust force, the displacement and the acceleration. The processing of these signals demonstrated that the damage is due to the combination of two main factors: the spring-back of the thin part and the thrust force. The results found were confirmed for different feeds and speeds. When the distance between supports is increased, it is observed that the spring-back increases but the thrust force decreases. The study proves the feasibility of unsupported drilling of thin CFRP laminates without creating any observable damage.