Using static light scattering (SLS) and small-angle neutron scattering (SANS) in conjunction with rheological measurements, the significance of electrostatic interactions and micellar microstructure to the formation of shear-induced structures (SIS) in systems of dilute aqueous cylindrical micelles is investigated. This is accomplished through a systematic study of the influence of increasing NaCl concentration on the dilute aqueous micellar system of 11 mM cetyltrimethylammonium p-toluenesulfonate (CTAT). Concurrent with increases in the zero-shear viscosity (eta(o)), low NaCl concentrations lead to the growth of micelles through increases in the degree of screening of electrostatic interactions. These systems, which exhibit discernible electrostatic or correlation peaks in the SANS results, undergo shear-induced structural transitions, whereby critical shear rates tend to increase with NaCl concentration. With further increases in the NaCl concentration, intermicellar electrostatic interactions are adequately screened, and no SIS is observed. The addition of NaCl to these systems increases the micellar flexibility, as shown by SLS. The eta(o), of these systems decreases, and the critical shear rates for these shear-thinning systems increases, consistent with expectations for dilute polyelectrolyte systems.