Abstract: A pressure-sensitive adhesive that has high cohesive strength and adheres permanently to high-solids automotive paint systems preferably comprises a mixture of (1) a crosslinked acrylic copolymer of acrylic acid ester and N-vinyl-2-pyrrolidone, and (2) certain tackifier resins. Useful tackifier resins are poly(isobornylmethacrylate), pentaerythritol ester of rosin, and mixed-aliphatic/aromatic polymeric tackifier resins such as a t-butylated styrene. The tackifier resin preferably has a T.sub.g of at least 30.degree. C., M.sub.n from 300 to 3000, and a solubility parameter from 8 to 9. The novel pressure-sensitive adhesive is particularly useful as a dense surface layer of a composite tape having a foamlike core.