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 SL≤40 000 MPa·mm with





S
⁢
L

=

max
⁢


(



Δ
⁢

σ
bending_CI


Cp

;


Δ
⁢

σ
bending_CE




C
r

×
Cp



)






and a size criterion Ec≥0.46 with Ec=Sc/Se.