Composite cap which is to be fixed to the glass ring of a bottle and then serve as a stopper which can be screwed and unscrewed as desired in order to close or open the distribution orifice of said bottle, said glass ring being provided with at least one annular protuberance, said composite cap comprising: - a shell, typically made of metal, having a substantially cylindrical skirt, provided with an inner annular protuberance; - a first insert, arranged inside said shell, rigidly connected to said shell, comprising a skirt provided with an inner screw thread, - a second insert in the general shape of a sleeve having at least two generally cylindrical portions (31 and 32); - the first portion being provided on the external wall thereof with a screw thread which is complementary to that of said first insert, so that said first insert and said second insert are in the form of an assembly (20 + 30) rigidly connected by screwing, located inside said shell; - the second portion being provided with axial immobilisation means which are to cooperate with said annular protuberance of said ring, and with axial stop means, typically the lower end of said second portion, which cooperate with said inner annular protuberance so that said assembly (20 + 30) which is rigidly connected by screwing is trapped inside said shell, characterised in that said first portion of the second insert has a height such that, when said composite cap is rigidly connected in an irreversible manner to said glass ring, the upper end thereof is located beneath the level of the rim of the ring, and said first insert comprises a head which extends transversely with respect to said skirt, said cap also comprising a seal placed inside the first insert and having a diameter such that it remains trapped between said head of the first insert and the upper end of said first portion of the second insert. - a shell, typically made of metal, having a substantially cylindrical skirt, provided with an inner annular protuberance; - a first insert, arranged inside said shell, rigidly connected to said shell, comprising a skirt provided with an inner screw thread, - a second insert in the general shape of a sleeve having at least two generally cylindrical portions (31 and 32); - the first portion being provided on the external wall thereof with a screw thread which is complementary to that of said first insert, so that said first insert and said second insert are in the form of an assembly (20 + 30) rigidly connected by screwing, located inside said shell; - the second portion being provided with axial immobilisation means which are to cooperate with said annular protuberance of said ring, and with axial stop means, typically the lower end of said second portion, which cooperate with said inner annular protuberance so that said assembly (20 + 30) which is rigidly connected by screwing is trapped inside said shell, characterised in that said first portion of the second insert has a height such that, when said composite cap is rigidly connected in an irreversible manner to said glass ring, the upper end thereof is located beneath the level of the rim of the ring, and said first insert comprises a head which extends transversely with respect to said skirt, said cap also comprising a seal placed inside the first insert and having a diameter such that it remains trapped between said head of the first insert and the upper end of said first portion of the second insert.