The rolling resistance of a tire has been improved without degrading industrial performance. The sidewall (30) consists of two sub-layers. A first sub-layer (FE1) of thickness E1 and volume V1 provides the expected protection functions of a sidewall as the outer wall of the tire, and a second sub-layer of the sidewall (FE2) of thickness E2 and volume V2 is optimized at low hysteresis to improve rolling resistance. The ratio V1/(V1+V2) of the volumes of the two sub-layers (FE1, FE2) is less than or equal to 0.3. The elongation at break of the compound of FE1 is greater than or equal to 200% measured at a temperature of 100 C., and the viscoelastic loss of the compound of FE2, Tan()max, is less than or equal to 0.10.