The invention describes an anhydrous cosmetic composition for nail varnish, comprising at least one cosmetically acceptable organic solvent, at least one cellulose-derived film-forming agent and an effective amount of at least one gloss-improving agent, the gloss-improving agent(s) being a copolymer via condensation of adipic acid and of pentaerythritol comprising end groups of caproic acid, of heptanoic acid, of caprylic acid and/or of capric acid; or a mixture of a plurality of these copolymers. Furthermore, the invention relates to the use of said copolymers as a gloss-improving agent in an anhydrous cosmetic composition, and also to a method for preparing such an anhydrous cosmetic composition for nail varnish.