Statistical copolymer films that consist of two types of monomers, a sticky and a glassy monomer, are investigated. These model systems of pressure-sensitive adhesive films are probed with X-ray reflectivity and mechanical tack measurements. For the first time, composition profiles along the surface normal in the near-surface region are monitored. The influence of the type of monomers being copolymerized, the monomer ratio, and the sample age on the near-surface composition as well as the resulting adhesive performance of the films are analyzed. The copolymers contain ethylhexyl acrylate as the majority component and styrene, maleic acid anhydride, or methylmethacrylate as a minority component. Regardless of the composition, we find a surface enrichment of one component in all samples. In the case of freshly prepared samples, this enrichment is driven by solubility due to the preparation based on solution casting. The minimization of the surface free energy results in an internal reorganization and the component of the statistical copolymer with the lower surface tension enriches at the free surface. The mechanical behavior is not dominated by the surface but by the surface-near part of the composition profile.