Starting from a process for producing a rod-like preform, in particular for optical fibers, in which a tubular blank whose refractive index changes, viewed in the radial direction is fed to a heating zone, is softened there, and in the softened state is shaped to give the preform, a method is described for producing preforms which are hyperpure and low in defects, in which the blank used is one whose refractive index decreases, viewed in the radial direction, from the outside inwards, starting from at least one interface which is at a sufficient distance from the outer surface of the blank, of which that part which has been softened in the heating zone is introverted apart from an outer skin, and by which the preform is formed in the longitudinal axis of the tubular blank, counter to the direction in which the latter is fed to the heating zone, and in which the remaining outer skin is drawn off as a rod in the feed direction of the blank.