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Strained-layer Ga0.7In0.3As-AlGaAs-GaAs graded-index separate-confinement heterostructure single-quantum-well lasers were grown by molecular-beam epitaxy with growth conditions selected to optimize the growth of each material. The lasers emit at a wavelength of 1.03 mu m at 300 K, have threshold currents of 12 mA for 3 mu m*400 mu m devices, and have average threshold current densities of 174 A/cm2 for 40 mu m*800 mu m devices. Studies of threshold current versus cavity length and width agree with theoretical formulations. The threshold currents for lasers of various lengths and widths are significantly lower than those for previous strained-layer lasers grown by molecular-beam epitaxy and lower than those for strained-layer lasers grown by organometallic vapor-phase epitaxy. Although these devices have not been optimized for microwave modulation, 4-GHz bandwidths have been measured for 21.5 mu m*600 mu m devices.