An optical fiber having a core and an outer cladding, the core including from its center outward a central core having a radius and a refractive index difference with respect to the outer cladding, and a depressed inner cladding. The depressed inner cladding includes at least a first portion having a radius and a refractive index difference with respect to the outer cladding, the first portion preferably being adjacent to the central core, and a second portion adjacent to the first portion constituting a depressed trench having a radius, and a refractive index difference with respect to the outer cladding. The first portion of the inner cladding has a refractive index below the refractive index of the outer cladding, and the depressed trench has a refractive index that is lower than the refractive index of the first portion of the depressed inner cladding. The outer radius of the depressed inner cladding of the optical fiber is between 28 μm and 40 μm, the LP01 mode leakage losses at a wavelength of 1550 nm are less than 0.01 dB/km and the cable cut-off wavelength is less than 1530 nm.