The tire has a carcass reinforcement which has at least one layer and a crown reinforcement that is capped radially by a tread. The tire also includes a layer P of polymer compounds in contact with at least one working crown layer and in contact with the carcass reinforcement. The elastomer compounds forming the calendering layer, radially outermost with respect to the crown of the tire, of the carcass reinforcement layer have a relative density of sulfur bridges of less than 5%. The elastomer compounds forming the layer P have a relative density of sulfur bridges of less than 5%. The elastomer compounds are compositions based on at least one diene elastomer selected from the group of polybutadienes (BRs), synthetic polyisoprenes (IRs), natural rubber (NR), isoprene copolymers, butadiene copolymers with the exception of butadiene-nitrile copolymers (NBRs), apart from diene elastomers bearing carboxyl functions, and mixtures of these diene elastomers.