Tire, the internal wall of which is covered with an airtight layer, itself covered with a layer of self-sealing product, comprising a radial carcass reinforcement (60) composed of reinforcing elements (61) having an elongation at break EBC and a breaking strength BSC, placed at a placement pitch PC and coated with rubber composition, designed so as to satisfy the inequality: BS C P C ≤ 1.5 · 10 6 · ( R S 2 - R E 2 ) R T , each sidewall of the tire additionally comprising an additional strengthening reinforcement (120) composed of thread reinforcing elements having an elongation at break EBA and a breaking strength BSA, placed at a placement pitch PA and coated with rubber composition, in which each of the two additional strengthening reinforcements is designed such that: BS A P A ≥ 1.3 · BS C P C , and EBC≧EBA, the breaking strengths BSA and BSC and the elongations at break EBC and EBA being determined on the reinforcing elements after extraction from the cured tire.