Colloidal quantum dots (CQDs) feature a low degeneracy of electronic states at the band edges compared with the corresponding bulk material1, as well as a narrow emission linewidth2,3. Unfortunately for potential laser applications, this degeneracy is incompletely lifted in the valence band, spreading the hole population among several states at room temperature4,5,6. This leads to increased optical gain thresholds, demanding high photoexcitation levels to achieve population inversion (more electrons in excited states than in ground states—the condition for optical gain). This, in turn, increases Auger recombination losses7, limiting the gain lifetime to sub-nanoseconds and preventing steady laser action8,9. State degeneracy also broadens the photoluminescence linewidth at the single-particle level10. Here we demonstrate a way to decrease the band-edge degeneracy and single-dot photoluminescence linewidth in CQDs by means of uniform biaxial strain. We have developed a synthetic strategy that we term facet-selective epitaxy: we first switch off, and then switch on, shell growth on the (0001) facet of wurtzite CdSe cores, producing asymmetric compressive shells that create built-in biaxial strain, while still maintaining excellent surface passivation (preventing defect formation, which otherwise would cause non-radiative recombination losses). Our synthesis spreads the excitonic fine structure uniformly and sufficiently broadly that it prevents valence-band-edge states from being thermally depopulated. We thereby reduce the optical gain threshold and demonstrate continuous-wave lasing from CQD solids, expanding the library of solution-processed materials11,12that may be capable of continuous-wave lasing. The individual CQDs exhibit an ultra-narrow single-dot linewidth, and we successfully propagate this into the ensemble of CQDs.