We demonstrate that nonionic polymer can be used to control the shear-induced transition observed in the cationic rodlike micellar system of cetyltrimethylammonium p-toluene sulfonate (CTAT). Hydroxypropyl cellulose (HPC) suppresses this transition, while poly(ethylene oxide) (PEO) enhances the zero-shear viscosity, with little change to the critical rates of the transition. It is proposed that the availability of hydrophobic moieties of HPC allows for its influence on the onset of the transition. This is consistent with binding, rheological, and small-angle neutron scattering (SANS) studies. Furthermore, quiescent SANS shows that both polymers affect intermicellar interactions, solvent-micelle interactions, and/or micellar length. While the onset of the shear-induced transition may be altered with polymer, polymer composition does not affect micellar flexibility and/or interactions in the aligned transitioned state.