Disclosed is a single mode optical waveguide fiber having a core refractive index profile in which the profile parameters are selected to provide an attenuation minimum. A set of profiles having the same general shape and dimensions is shown to have a group of profiles contained in a sub-set which exhibit a minimum of attenuation as compared to the remaining members of the set. The members of the sub-set have been found to have the lowest effective group index, n.sub.geff, and the lowest change in .beta..sup.2 under waveguide fiber bending.