A multi-strand cord (50) comprises an internal layer (CI) of the cord made up of K=1 two-layer (C1, C3) internal strand (TI), with the internal layer (C1) being made up of Q internal metallic threads (F1), and the external layer (C3) being made up of N external metallic threads (F3), and an external layer (CE) of the cord made up of L>1 two-layer (C1, C3) external strands (TE) wound around the internal layer (CI) of the cord, with the internal layer (C1) being made up of Q internal metallic threads (F1), and the external layer (C3) being made up of N external metallic threads (F3). The cord (50) has an endurance criterion SL40 000 MPa.Math.mm with $SL=\max \left(\frac{{}_{\mathrm{bending\_CI}}}{\mathrm{Cp}};\frac{{}_{\mathrm{bending\_CE}}}{C_r\mathrm{Cp}}\right)$
and a size criterion Ec0.46 with Ec=Sc/Se.

A multi-strand cord (50) comprises an internal layer (CI) of the cord made up of K=1 three-layer (C1, C2, C3) internal strand (TI), with the internal layer (C1) being made up of Q internal metallic threads (F1), the intermediate layer (C2) being made up of M intermediate metallic threads (F2) and the external layer (C3) being made up of N external metallic threads (F3), and an external layer (CE) of the cord made up of L>1 three-layer (C1, C2, C3) external strands (TE) wound around the internal layer (CI) of the cord, with the internal layer (C1) being made up of Q internal metallic threads (F1), the intermediate layer (C2) being made up of M intermediate metallic threads (F2) and the external layer (C3) being made up of N external metallic threads (F3). The cord (50) has an endurance criterion SL40 000 MPa.Math.mm with $SL=\max \left(\frac{{}_{\mathrm{bending}\_\mathrm{CI}}}{\mathrm{Cp}};\frac{{}_{\mathrm{bending}\_\mathrm{CE}}}{C_r\mathrm{Cp}}\right);$
and a size criterion Ec0.46 with Ec=Sc/Se.