An optical fiber preform is assembled by inserting core rod segments axially end to end inside of a first glass overclad tube having a first, relatively low concentration of a given impurity that contributes to signal attenuation in an optical fiber to be drawn from the preform. The first overclad tube with the contained core rod segments are inserted in a second glass tube having a second concentration of the given impurity which is higher than the first concentration. The wall thickness of the first overclad tube is preferably less than that of the second overclad tube, thus reducing the amount of high purity glass needed to form the first overclad tube and attendant manufacturing costs. The core rod segments may include salvageable remnants from a single long core rod produced, for example, by vapor axial deposition (VAD).