Threshold current densities as low as 80 A/cm**2 for 3. 3 mm-long cavity lasers, and 93 A/cm**2 for 520 mu m-long cavity lasers have been obtained in AlGaAs/GaAs graded-index separate-confinement heterostructure (GRINSCH) single-quantum-well lasers with quantum-well widths between 65-165 A grown by molecular beam epitaxy. The structures were prepared on (100) GaAs substrates and do not display the earlier reported dependence of lasing threshold characteristics on the quantum-well thickness in the range studied (65-165 A).