A tire comprising two beads, a crown and sidewalls that connect the crown to said beads, the tire being reinforced by a carcass reinforcement anchored in each bead to at least one annular anchoring element, each sidewall comprising an additional, inextensible sidewall ring located axially inside the axially outermost carcass ply and a coupling section located radially between the annular anchoring element in the bead and said sidewall ring and positioned axially inside the axially outermost carcass ply. The tire is characterized in that the line segments passing through the centers of gravity of the sections of the annular anchoring rings in the beads and through the center of gravity of the sidewall rings on the same respective side, make angles respectively of β1 and β2 relative to the rotation axis, these angles being different.