The steering properties of four types of stationary discrete bright staggered solitons, on-site, inter-site, twisted inter-site, and twisted on-site, in self-defocusing photovoltaic photo-refractive media are investigated by introducing transversal perturbations. Because of the translational symmetry between on-site and inter-site localized modes they are considered as two dynamical realizations of the same moving mode. The exchange between trapping and steering of these modes is interpreted by the Peierls-Nabarro formalism. The twisted inter-site and on-site localized modes are transformed by a transversal perturbation into trapped on-site modes of lower power and radiation. ©2005 Optical Society of America.