Data are presented on photopumped single- and multiple-quantum-well Al
xGa
1-xAs-GaAs heterostructures grown by metalorganic chemical vapor deposition (MO-CVD) showing that continuous room-temperature (CW 300 K) laser operation of such structures is possible in the range 0-150 meV above the GaAs active region band edge (

meV). Optically pumped multiple-quantum-well heterostructure lasers of short cavity length (

m), and thus high edge-to-edge cavity end losses, are shown to operate at photo-excitation threshold levels as low as 900 W/cm
2(

A/cm
2). As the quantum-well dimension is reduced to

Å, single-active-layer heterostructures shift their laser operation to higher confined-particle states, or fail to operate altogether, whereas multiple-active-layer heterostructures continue to operate as lasers on the lowest confined-particle states

and

transitions). For a multiple-quantum-well heterostructure of small enough GaAs active region size,

Å, recombination radiation at the energy gap is cut off, and as expected, laser operation on the lowest confined-particle states (1 - 1\´) is shifted to high energy (

meV).