Two-layer multi-strand cord, comprises: - an internal layer of the cord made up of K>1 internal strands wound in a helix, each internal strand being a three-layer (C1, C2, C3) strand and comprising: • an internal layer made up of Q=2, 3 or 4 internal threads wound with a pitch p1, the internal layer being wound in an internal-layer direction of each internal strand, • an intermediate layer made up of M intermediate threads, wound around the internal layer with a pitch p2, the intermediate layer being wound in an intermediate-layer direction of each internal strand, and • an external layer made up of N external threads wound around the intermediate layer with a pitch p3, - an external layer of the cord made up of L>1 external strands wound around the internal layer of the cord, each external strand being an at least two-layer (C1', C3') strand and comprising: • an internal layer (C1') made up of Q' internal thread(s) (F1'), and • an external layer (C3') made up of N' external threads (F3') wound around the internal layer (C1'), wherein: - p1 is different from p2 and/or the internal-layer direction of each internal strand is different from the intermediate-layer direction of each internal strand; - the intermediate layer of each internal strand is desaturated; - the external layer of each internal strand is desaturated; and characterized in that: - the pitches p2 and p3 satisfy the relationship: - 0.36 ≤ (p3-p2)/p3≤ 0.45 in instances in which Q=2, - 0.36 ≤ (p3-p2)/p3≤ 0.42 in instances in which Q=3, - 0.36 ≤ (p3-p2)/p3 ≤ 0.43 in instances in which Q=4 and the mean inter-strand distance E separating two adjacent external strands is greater than or equal to 150 μm. - an internal layer of the cord made up of K>1 internal strands wound in a helix, each internal strand being a three-layer (C1, C2, C3) strand and comprising: • an internal layer made up of Q=2, 3 or 4 internal threads wound with a pitch p1, the internal layer being wound in an internal-layer direction of each internal strand, • an intermediate layer made up of M intermediate threads, wound around the internal layer with a pitch p2, the intermediate layer being wound in an intermediate-layer direction of each internal strand, and • an external layer made up of N external threads wound around the intermediate layer with a pitch p3, • an internal layer made up of Q=2, 3 or 4 internal threads wound with a pitch p1, the internal layer being wound in an internal-layer direction of each internal strand, • an intermediate layer made up of M intermediate threads, wound around the internal layer with a pitch p2, the intermediate layer being wound in an intermediate-layer direction of each internal strand, and • an external layer made up of N external threads wound around the intermediate layer with a pitch p3, - an external layer of the cord made up of L>1 external strands wound around the internal layer of the cord, each external strand being an at least two-layer (C1', C3') strand and comprising: • an internal layer (C1') made up of Q' internal thread(s) (F1'), and • an external layer (C3') made up of N' external threads (F3') wound around the internal layer (C1'), • an internal layer (C1') made up of Q' internal thread(s) (F1'), and • an external layer (C3') made up of N' external threads (F3') wound around the internal layer (C1'), - p1 is different from p2 and/or the internal-layer direction of each internal strand is different from the intermediate-layer direction of each internal strand; - the intermediate layer of each internal strand is desaturated; - the external layer of each internal strand is desaturated; and characterized in that: - the pitches p2 and p3 satisfy the relationship: - 0.36 ≤ (p3-p2)/p3≤ 0.45 in instances in which Q=2, - 0.36 ≤ (p3-p2)/p3≤ 0.42 in instances in which Q=3, - 0.36 ≤ (p3-p2)/p3 ≤ 0.43 in instances in which Q=4 and the mean inter-strand distance E separating two adjacent external strands is greater than or equal to 150 μm. - the pitches p2 and p3 satisfy the relationship: - 0.36 ≤ (p3-p2)/p3≤ 0.45 in instances in which Q=2, - 0.36 ≤ (p3-p2)/p3≤ 0.42 in instances in which Q=3, - 0.36 ≤ (p3-p2)/p3 ≤ 0.43 in instances in which Q=4 and the mean inter-strand distance E separating two adjacent external strands is greater than or equal to 150 μm. - 0.36 ≤ (p3-p2)/p3≤ 0.45 in instances in which Q=2, - 0.36 ≤ (p3-p2)/p3≤ 0.42 in instances in which Q=3, - 0.36 ≤ (p3-p2)/p3 ≤ 0.43 in instances in which Q=4 and