New measurements of the birefringence induced in ultralow-birefringence fibers by a succession of orthogonally polarized UV side exposures show the reversibility of the process. Moreover, it is shown that the birefringence growth depends on two parameters, the total irradiation dose and the nature of the successive polarized UV side exposures. These observations indicate that geometric asymmetry is not the major cause of the birefringence and confirm a model of birefringence growth based on dipole alignment.