The radiation-induced Bragg wavelength shift (BWS) was measured with type I gratings made of 12 fibers with very different composition, i.e. of fibers with an extremely different radiation-induced attenuation. With two of the fibers fabrication parameters like laser intensity, hydrogen loading, and annealing conditions after grating inscription were varied. With another fiber type I and type II gratings were made by a completely different process. With gratings made under identical conditions of the twelve fibers the radiation-induced BWS only varied by about a factor of three. Varying the fabrication parameters led to BWS differences up to nearly a factor of ten.