Confinement quality as good as ELM-free H-mode at densities substantially above the Greenwald density limit ( &nmacr;(e,0)/n(GW) = 1.4) has been obtained in discharges with a radiative boundary under quasistationary conditions for 20 times the energy confinement time. This is achieved by optimizing the gas-fueling rate of RI-mode discharges which tailors their favorable energy confinement and leads to discharges with beta values just below the operational limit beta(n) = 2 of TEXTOR-94, thereby effectively avoiding confinement back transitions or disruptions. In addition, this high-density regime is favorable for helium removal and results in figures of merit tau(*)(p,He)/tau(E) approximately 10-15, relevant for a future fusion power reactor.