Tyre comprising: two beads designed to come into contact with a mounting rim, each bead comprising at least one annular reinforcing structure having a radially innermost point; two sidewalls extending from the two beads radially outwards, the two sidewalls joining together in a crown; a carcass reinforcement extending from one bead to the other, passing through the crown, the carcass reinforcement being anchored in each bead to said at least one annular reinforcing structure; the tyre having an outer profile such that, for at least one of the two sidewalls, in any radial section, the distance between the carcass reinforcement and the outer profile, measured between a point of the carcass reinforcement and the point of intersection between the outer profile and a direction perpendicular to the carcass reinforcement passing through this point of the carcass reinforcement, achieves a minimum value DM at a first point of the carcass reinforcement having a radial distance HD greater than or equal to 0.50·H and less than or equal to 0.75·H from the radially innermost point of the annular reinforcing structure, H being the radial height of the tyre; wherein the tangent at the carcass reinforcement at the first point is inclined at an angle (β) that is greater than or equal to 5° and less than or equal to 32° relative to a radial direction; wherein there is a first zone of the carcass reinforcement comprising the first point of the carcass reinforcement, such that, for each point of the first-zone, the radius of curvature RCC of the carcass reinforcement is less than the radius of curvature RCO of the outer profile at the point of intersection between the outer profile and a direction perpendicular to the carcass reinforcement passing through this point of the first-zone, such that RCO > 1.2·RCC; characterized in that there is a second zone of the carcass reinforcement, located radially inside the first zone, such that, for each point of the second-zone of the carcass reinforcement, the radius of curvature RCC of the carcass reinforcement is greater than the radius of curvature RCO of the outer profile at the point of intersection between the outer profile and a direction perpendicular to the carcass reinforcement passing through this point of the second-zone, such that RCO < 0.9·RCC, each point of the second-zone having a radial distance greater than or equal to 0.40·H from the radially innermost point of the annular reinforcing structure; it being understood that the angles, distances, thicknesses and radii of curvature are determined when the tyre is fitted to the mounting rim and inflated to its service pressure. two beads designed to come into contact with a mounting rim, each bead comprising at least one annular reinforcing structure having a radially innermost point; two sidewalls extending from the two beads radially outwards, the two sidewalls joining together in a crown; a carcass reinforcement extending from one bead to the other, passing through the crown, the carcass reinforcement being anchored in each bead to said at least one annular reinforcing structure; the tyre having an outer profile such that, for at least one of the two sidewalls, in any radial section, the distance between the carcass reinforcement and the outer profile, measured between a point of the carcass reinforcement and the point of intersection between the outer profile and a direction perpendicular to the carcass reinforcement passing through this point of the carcass reinforcement, achieves a minimum value DM at a first point of the carcass reinforcement having a radial distance HD greater than or equal to 0.50·H and less than or equal to 0.75·H from the radially innermost point of the annular reinforcing structure, H being the radial height of the tyre; wherein the tangent at the carcass reinforcement at the first point is inclined at an angle (β) that is greater than or equal to 5° and less than or equal to 32° relative to a radial direction; wherein there is a first zone of the carcass reinforcement comprising the first point of the carcass reinforcement, such that, for each point of the first-zone, the radius of curvature RCC of the carcass reinforcement is less than the radius of curvature RCO of the outer profile at the point of intersection between the outer profile and a direction perpendicular to the carcass reinforcement passing through this point of the first-zone, such that RCO > 1.2·RCC; characterized in that there is a second zone of the carcass reinforcement, located radially inside the first zone, such that, for each point of the second-zone of the carcass reinforcement, the radius of curvature RCC of the carcass reinforcement is greater than the radius of curvature RCO of the outer profile at the point of intersection between the outer profile and a direction perpendicular to the carcass reinforcement passing through this point of the second-zone, such that RCO < 0.9·RCC, each point of the second-zone having a radial distance greater than or equal to 0.40·H from the radially innermost point of the annular reinforcing structure; it being understood that the angles, distances, thicknesses and radii of curvature are determined when the tyre is fitted to the mounting rim and inflated to its service pressure.