Electron cyclotron current drive (ECCD) at a low power level has been used on Tore Supra to induce local perturbations of the current density profile. Regimes with strong MHD activity have been analysed, and compared with similar stable discharges, in order to investigate the possible causes of their instability and relate the evolution of the discharge to the localization of EC power deposition. Both co- and counter-current drive pulses have been applied to dominantly or fully non-inductive discharges, sustained by a lower hybrid current drive. Detailed reconstructions by current diffusion calculations have been performed and the error bars evaluated. This method has proved valuable for shedding light on the complex interplay between the evolutions of temperature and safety factor profiles in steady-state tokamak plasmas. The crucial role of the dynamic evolution of rational surfaces has been identified. Moreover, we demonstrate that the operational domain in which ECCD can be employed must cope with the overall current profile characteristics, in particular the position where the safety factor has a minimum.