The present invention relates to an anhydrous solid cosmetic composition comprising: a) at least one non-volatile phenyl silicone first oil not bearing any dimethicone fragments; b) at least one non-volatile phenyl silicone second oil bearing at least one dimethicone fragment; c) at least one vinyl polymer comprising at least one carbosiloxane dendrimer-based unit. The invention also relates to a process for making up and/or caring for the lips, in which the abovementioned composition is applied to the lips.