We recently reported the observation of transverse Anderson localization as the waveguiding mechanism in optical fibers with random transverse refractive index profiles [Opt. Lett. 37, 2304 (2012)]. Here, we explore the impact of the design parameters of the disordered fiber on the beam radius of the propagating transverse localized beam. We show that the optimum value of the fill-fraction of the disorder is 50% and a lower value results in a larger beam radius. We also explore the impact of the average size of the individual random features on the value of the localized beam radius and show how the boundary of the fiber can impact the observed localization radius. A larger refractive index contrast between the host medium and the disorder sites results in smaller value of the beam radius.