A single-mode optical fiber suitable for the transmission of solitons has a refractive index profile that changes along the length of the fiber to provide a fiber dispersion that monotonically decreases along the fiber from one end thereof to the other. The fiber includes a core of maximum refractive index n.sub.1 and a radius a, surrounded by cladding material having a refractive index n.sub.2 which is less than n.sub.1. The fiber core includes a central region that extends to the longitudinal axis of the fiber and an outer region, the inner and outer regions being separated by a region of depressed refractive index. The inner radius a.sub.1 of the region of depressed refractive index is greater than zero and the maximum radius a.sub.o of the region of depressed refractive index is less than a. The fiber preform can be made by depositing layers of glass particles on an elongated mandrel, the composition of glass particles being varied with respect to longitudinal position along the preform during the deposition of some of the layers.