Tire (10) for a heavy goods vehicle comprising a radial carcass reinforcement (60) anchored in each of the beads (50) to an anchoring structure (700), comprising a circumferential reinforcement (70), the carcass reinforcement (60) being partially wrapped around the anchoring structure (700), the tire (10) also comprising a coupling reinforcement (150) comprising a first part (151) in contact with the carcass reinforcement (60) and being extended by a second part (152) in contact with the anchoring structure (700) as far as a point (157) radially on the outside of the anchoring structure (700), located axially between the axially inner-most point (702) and the axially outermost point (704) of the anchoring structure (700), the tire (10) also comprising a stiffening reinforcement (160) surrounding the coupling reinforcement (150) and running radially on the inside of the anchoring structure (700) and of the coupling reinforcement (150), in which the axially outside end point (166) of said stiffening reinforcement (160) is located at a radial distance DR from the radially innermost point (73) of the circumferential reinforcement (70), the radial distance DR being greater than or equal to 0.8 times the radial distance DS between the radially innermost and radially outermost points (71, 73) of the circumferential reinforcement (70) and less than or equal to 1.2 times the radial distance DS.