Tyre having a radial carcass reinforcement, composed of at least one layer of reinforcing elements inserted between two calendaring layers of elastomeric mixture, the said tyre comprising a crown reinforcement, itself topped radially by a tread, the said tread being joined to two beads via two sidewalls, characterized in that the metal reinforcing elements (27, 37, 47) of at least one layer of the carcass reinforcement are cords exhibiting, in the "permeability" test, a flow rate of less than 20 cm 3 /min, in that at least one layer of the carcass reinforcement is provided, on at least one face, with textile threads (20, 30, 40) and in that at least the layer of elastomeric mixture, radially external to the bead wire and in contact with the latter, is an elastomeric mixture based on natural rubber or on synthetic polyisoprene having a majority of cis-1,4- enchainments and optionally on at least one other diene elastomer, the natural rubber or the synthetic polyisoprene, in the case of a blend, being present at a predominant content with respect to the content of the other diene elastomer or elastomers used, and on a reinforcing filler composed: (i) either of a white filler of silica and/or alumina type comprising SiOH and/or AlOH surface functional groups, selected from the group consisting of precipitated or fumed silicas, aluminas and aluminosilicates, or alternatively carbon blacks modified during or after the synthesis so as to at least partially cover their surface with SiOH and/or AlOH functional groups, having a specific surface of between 30 and 260 m 2 /g, employed at a content of greater than or equal to 15 phr and less than or equal to 55 phr, (ii) or of a blend of carbon black having a BET specific surface between 30 and 160 m 2 /g and a white filler described in (i), in which the overall content of filler is greater than or equal to 15 phr and less than or equal to 60 phr and the content in phr of white filler is greater than or equal to the content of carbon black in phr minus 5, the BET specific surface measurement is carried out according to the Brunauer, Emmett and Teller method described in The Journal of the American Chemical Society, Vol. 60, page 309, February 1938, corresponding to Standard NFT 45007 ofNovember 1987. (i) either of a white filler of silica and/or alumina type comprising SiOH and/or AlOH surface functional groups, selected from the group consisting of precipitated or fumed silicas, aluminas and aluminosilicates, or alternatively carbon blacks modified during or after the synthesis so as to at least partially cover their surface with SiOH and/or AlOH functional groups, having a specific surface of between 30 and 260 m 2 /g, employed at a content of greater than or equal to 15 phr and less than or equal to 55 phr, (ii) or of a blend of carbon black having a BET specific surface between 30 and 160 m 2 /g and a white filler described in (i), in which the overall content of filler is greater than or equal to 15 phr and less than or equal to 60 phr and the content in phr of white filler is greater than or equal to the content of carbon black in phr minus 5, the BET specific surface measurement is carried out according to the Brunauer, Emmett and Teller method described in The Journal of the American Chemical Society, Vol. 60, page 309, February 1938, corresponding to Standard NFT 45007 ofNovember 1987.