The invention relates to a tyre having a radial carcass reinforcement, consisting of at least one layer of metal reinforcing elements, said tyre comprising a crown reinforcement, which is itself covered radially with a tread, said tread being joined to two beads via two sidewalls. According to the invention, the metal reinforcing elements of at least one layer of the carcass reinforcement are non-hooped cords having, in the permeability test, a flow rate of less than 20 cm3/min and, in a radial plane, at least over part of the meridian profile of the tyre, the thickness of the rubber compound between the inner surface of the cavity of the tyre and that point of a metal reinforcing element of the carcass reinforcement which is closest to said inner surface of the cavity is less than or equal to 3.5 mm and the ratio between the thicknesses of rubber compound between the inner surface of the cavity of the tyre and that point of a metal reinforcing element of the carcass reinforcement which is closest to said inner surface of the cavity of two distinct parts of the tyre is greater than 1.15. FIG. la
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