A process for making a non-zero dispersion shifted optical fiber having low splice loss and low attenuation and to an optical fiber produced by this process. A reduction of the splice loss is observed with decreasing drawing tension. The optical fiber has a core region that includes three segments and an inner cladding segment, each having a maximum refractive index percent difference, Δdeltai %, i=0-3, the subscript i referring to a particular refractive index, the core segments being selected such that Δdelta0%>Δdelta2%>Δdelta1%≧0 and Δdelta2%>Δdelta3%≧0. Optical fibers exhibiting low splice loss were drawn at tensions not larger than 150 g, preferably not larger than 100 g.