Metal cord with three layers (C1+C2+C3) of 3+M+N construction, rubberized in situ, comprising a first layer or central layer (C1) comprised of three wires of diameter d1 assembled in a helix at a pitch p1, around which central layer there are wound in a helix at a pitch p2, in a second layer (C2), M wires of diameter d2, around which second layer there are wound in a helix at a pitch p3, in a third layer (C3), N wires of diameter d3. The cord has the following characteristics (d1, d2, d3, p1, p2 and p3 being expressed in mm): 0.08≦d1≦0.50; 0.08≦d2≦0.50; 0.08≦d3≦0.50; 3