Lower hybrid enhanced performance (LHEP) discharges have been successfully operated on Tore Supra, with a significant improvement in electron core-confinement and remarkable steady-state features. However, recent attempts to operate such discharges with better confinement performance were hindered by the systematic onset of large MHD activity, preventing any good performance recovery. The associated MHD limit is found to result from reaching the tearing mode limit as the current profile is driven from centrally peaked towards off-axis peaked by the lower hybrid (LH) wave. The specific feature of the considered discharges is that they achieve a weak magnetic shear over a broader core region than past LHEP discharges, then leading to systematic fast MHD onset (m/n = 2/1 tearing mode) when qmin approaches 2. The present paper reports on experimental observations and modelling which support this finding and analyses the perspectives of improving the LHEP scenario by combining the current profile control through the LH wave with a significant increase in pressure through ion cyclotron wave coupling.