Tire (1) for an off-road vehicle, comprising a crown and a tread (22) having a width W and a thickness E of wearable material, this tread (22) having a superposition of at least two layers of materials, a first layer (221) radially on the inside and a second layer (222) radially on the outside of the first layer (221) to contact the ground when the tire is new, this second layer (222) having a thickness E2 relative to the thickness E of wearable material, the tread (22) being provided with at least two narrow grooves (4, 5) running all around the tire which have a zigzagging shape of wavelength L and amplitude A, the wavelength L being between 10% and 120% of the axial width W of the tread (22), and the amplitude A being between 10% and 75% of axial width W. The material of the first layer (221) is chosen with low hysteresis; with a measured tan(δ) value at most equal to 0.30.