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 DMI 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 to the radially innermost point of the annular reinforcing structure, H being the radial height of the tyre, the minimum value DMI being greater than or equal to 1.0 mm and less than or equal to 2.5 mm; wherein there is a first zone of the carcass reinforcement, surrounding the first point of the carcass reinforcement, wherein the distance between the carcass reinforcement and the outer profile, measured between a point of the first-zone 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, increases continuously while moving away from the first point of the carcass reinforcement, radially inward and radially outward; wherein the first zone of the carcass reinforcement has, in any radial section, a radially inner end wherein the distance DMA between the carcass reinforcement and the outer profile, measured between the point of the carcass reinforcement forming this first radially inner end and the point of intersection between the outer profile and a direction perpendicular to the carcass reinforcement passing through this first radially inner end, is equal to or greater than 1.3.DMI; characterized in that there is a second zone of the carcass reinforcement which is adjacent to and radially inside of the first zone of the carcass reinforcement, wherein the distance between the carcass reinforcement and the outer profile, measured between a second-zone 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 second-zone point of the carcass reinforcement, is constant or decreases continuously while moving further away from the radially inner end point of the first zone; wherein the second zone of the carcass reinforcement has, in any radial section, a second radially inner end, DMD designating the distance between the carcass reinforcement and the outer profile, measured between the point of the carcass reinforcement forming this second radially inner end and the point of intersection between the outer profile and a direction perpendicular to the carcass reinforcement passing through this second radially inner end; wherein there is a third zone of the carcass reinforcement, which is adjacent to and radially on the inside of the second zone of the carcass reinforcement, wherein, at any point in the third zone, the distance between the carcass reinforcement and the outer profile, measured between a third-zone 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 third-zone point of the carcass reinforcement is greater than the distance DMD; and wherein the second zone of the carcass reinforcement has a radial height which is greater than or equal to 0.05·H. 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;