Single quantum well, graded refractive index separate confinement heterostucture (SQW GRINSCH) lasers with well thicknesses in the range of 65–480 A˚ have been grown by molecular beam epitaxy (MBE) on (100) and off of (100) by 4° toward (111)Asubstrates. The threshold current density appears to be independent of the well thickness in the range of 65–165 A˚ due to the compensating effects of volume of inversion and optical confinement. Under optimum growth conditions, the tilted substrates led to lower threshold current densities, the lowest value being 93 A/cm2for a 520‐&mgr;m‐long cavity laser with a 125‐A˚‐thick well. To our knowledge, this is by far the best ever reported threshold current density obtained in a semiconductor injection laser. Deviations from optimum growth conditions drastically increased the threshold current density on (100) substrates whereas the degradation for those on the tilted substrates was much less pronounced.