Tyre for a vehicle, said tyre being an essentially toroidal structure, defining three main directions: circumferential, axial and radial, comprising a crown comprising a tread, two sidewalls, and two beads, each sidewall connecting each bead to the crown, a carcass reinforcement anchored in each of the beads and extending in the sidewalls and in the crown, a crown reinforcement extending in the crown in the circumferential direction and situated radially between the carcass reinforcement and the tread, the crown reinforcement comprising a working reinforcement comprising at least first and second working plies (16, 18), each first and second working ply (16, 18) respectively comprising first and second reinforcing elements (50, 52) arranged substantially parallel to one another in each first and second working ply (16, 18), characterized in that at least one of the following relationships I or II is satisfied: 2500 ≤ D 1 4 × d 1 × 1000 / E 1 ≤ − 4672 × E 1 + 5444 and E 1 < 0.75 mm where: - D1 is the diameter of each first reinforcing element made up of a metallic monofilament, expressed in mm, with D1 ranging from 0.25 to 0.38 mm, - d1 is the density of the first reinforcing elements in the first working ply, expressed in monofilaments per decimetre and measured in a direction perpendicular to the main axis of the metallic monofilaments, - E1 is the mean thickness of the first working ply, expressed in mm and measured in the radial direction; 2500 ≤ D 2 4 × d 2 × 1000 / E 2 ≤ − 4672 × E 2 + 5444 and E 2 < 0.75 mm where - D2 is the diameter of each second reinforcing element made up of a metallic monofilament, expressed in mm, with D2 ranging from 0.25 to 0.38 mm, - d2 is the density of the second reinforcing elements in the second working ply, expressed in monofilaments per decimetre and measured in a direction perpendicular to the main axis of the metallic monofilaments, - E2 is the mean thickness of the second working ply, expressed in mm and measured in the radial direction; the characteristics D1, D2, d1, d2, E1, E2 being measured in the central part of the crown reinforcement of the tyre in the vulcanized state, on each side of the midplane over a total axial width of 4 cm. - D1 is the diameter of each first reinforcing element made up of a metallic monofilament, expressed in mm, with D1 ranging from 0.25 to 0.38 mm, - d1 is the density of the first reinforcing elements in the first working ply, expressed in monofilaments per decimetre and measured in a direction perpendicular to the main axis of the metallic monofilaments, - E1 is the mean thickness of the first working ply, expressed in mm and measured in the radial direction; 2500 ≤ D 2 4 × d 2 × 1000 / E 2 ≤ − 4672 × E 2 + 5444 and E 2 < 0.75 mm - D2 is the diameter of each second reinforcing element made up of a metallic monofilament, expressed in mm, with D2 ranging from 0.25 to 0.38 mm, - d2 is the density of the second reinforcing elements in the second working ply, expressed in monofilaments per decimetre and measured in a direction perpendicular to the main axis of the metallic monofilaments, - E2 is the mean thickness of the second working ply, expressed in mm and measured in the radial direction;