Extensive data are presented on various photopumped multiple‐quantum‐well AlxGa1−xAs‐GaAs heterostructures, grown by metalorganic chemical vapor deposition, showing the variety of laser operation that can be observed one and two phonons below the lowest (n=1,n′=1′) confined‐particle electron‐to‐heavy‐hole (e→hh,n) and electron‐to‐light‐hole (e→lh,n′) recombination transitions. These experiments are performed on small cleaved rectangular samples that, because of two identifiable sets of orthogonal coupled modes, permit unambiguous identification of laser operation on LO‐phonon sidebands below the confined‐particle transitions. For a small number (two) of closely coupled (∼50 A˚) GaAs quantum wells of sizeLz∼50 A˚ laser operation occurs on multiples of h&slash;&ohgr;LOfrom one phonon below transitionn=1 (E1) to within a phonon or two of theLindirect band edge. AlxGa1−xAs‐GaAs heterostructures with more coupled GaAs quantum wells readily permit observation of laser operationtwophonons below the lowest confined‐particle transitions. Besides the use of size to reduce carrier scattering to lower energies in a GaAs quantum well, high Zn doping is used to screen and reduce the electron‐phonon interaction and thus reduce the carrier scattering to lower energies. The strong phonon participation in the laser operation of these quantum‐well heterostructures, which are not superlattices, demonstrates that the electron‐phonon interaction observed in this work is a true two‐dimensional effect (and not, e.g., the effect of Brillouin‐zone folding). An analysis and arguments are presented justifying this statement and, in addition, leading to the important conclusion that stimulated phonon emission is possible and might play (or likely plays) a role in the quantum‐well heterostructures of this work.