Metal cord (C-1) with three layers (C1, C2, C3), which is rubberized in situ, comprising a core or first layer (10, C1) of diameter d1, around which there are wound together in a helix at a pitch p2, in a second layer (C2), N wires (11) of diameter d2, N varying from 5 to 7, around which there are wound together in a helix at a pitch p3, in a third layer (C3), P wires (12) of diameter d3, the said cord being characterized in that it has the following characteristics (d1, d2, d3, p2 and p3 being expressed in mm): 0.08≦d1≦0.40; 0.08≦d2≦0.35; 0.08≦d3≦0.35; 5π(d1+d2)