A quantum cascade laser utilizing non-resonant extraction design having a multilayered semiconductor with a single type of carrier; at least two final levels (1 and 1′) for a transition down from level 2; an energy spacing E21 greater than ELO; an energy spacing E31 of about 100 meV; and an energy spacing E32 about equal to ELO. The carrier wave function for level 1 overlaps with the carrier wave function for level 2. Likewise, the carrier wave function for level 1′ overlaps with the carrier wave function for level 2. In a second version, the basic design also has an energy spacing E54 of about 90 meV, and levels 1 and 1′ do not have to be spatially close to each other, provided that level 2 has significant overlap with both these levels. In a third version, there are at least three final levels (1, 1′, and 1″) for a transition down from level 2. Each of the levels 1, 1′, and 1″ has a non-uniform squared wave function distribution.