A glass body having a graded (substantially Gaussian) index profile is produced by a process that comprises providing a doped porous body (e.g., having a uniform dopant distribution), heat treating the porous body in a halogen-containing atmosphere, and consolidating the porous body into the glass body. The heat treatment removes a predetermined portion of the dopant from the porous body, such that the radial dopant profile in the glass body differs from the initial profile in the porous body, and such that the Gaussian index profile results. Exemplarily, the porous body is a uniformly germania-doped, VAD-produced, high-silica rod having radially decreasing density, and the heat treatment comprises an 8-hour densification soak at 1300.degree. C. in 20% Cl, 80% He. In a preferred embodiment, silica overcladding is deposited on a graded index core rod produced according to the invention, and fiber drawn from the resulting composite glass body.