Recent results on feedback control of the global shape of the current density profile in discharges with lower hybrid current drive (LHCD) on Tore Supra are presented. The global shape of the current density profile is characterized by its internal inductance li, and feedback controlled through the LH power or the launched LH wave spectrum. Feedback control of the flux on the plasma boundary has allowed for exploration of regimes with partial current drive (constant loop voltage) and full current drive (zero loop voltage). In stationary, steady state discharges at 0.8 MA (qa=7), the current profile shape is characterized by an li between 1.5 and 1.7 and a safety factor on-axis (q0) between 1 and 1.4. The energy confinement is 1.3 to 1.6 times higher than the value predicted by the Rebut-Lallia-Watkins scaling law