One embodiment of a single mode optical fiber includes: a graded index central core region having outer radius r1 and relative refractive index Δ1; a cladding region comprising (i) a first inner cladding region having an outer radius r2 10 microns and comprising a minimum relative refractive index Δ3, wherein said second inner cladding region has at least one region with a relative refractive index delta that becomes more negative with increasing radius; and (iii) an outer cladding region surrounding the second inner cladding region and comprising relative refractive index Δ4, wherein Δ1>Δ2>Δ3, Δ3