An optical transmission fiber is formed to include a relatively low-index, relatively thin outer cladding layer disposed underneath the protective polymer outer coating. Stray light propagating along an inner cladding layer(s) within the fiber will be refracted into the thin outer cladding (by proper selection of refractive index values). The thin dimension of the outer cladding layer allows for the stray light to "leak" into the outer coating in a controlled, gradual manner so as to minimize heating of the coating associated with the presence of stray light. The inventive fiber may also be bent to assist in the movement of stray light into the coating.