Colloidal quantum dots (CQDs) feature a low degeneracy of electronic states at the band edges compared with the corresponding bulk material(1), as well as a narrow emission linewidth(2,3). Unfortunately for potential laser applications, this degeneracy is incompletely lifted in the valence band, spreading the hole population among several states at room temperature(4-6). 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 losses(7), limiting the gain lifetime to sub-nanoseconds and preventing steady laser action(8,9). State degeneracy also broadens the photoluminescence linewidth at the single-particle level(10). 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 materials(11,12) that may be capable of continuous-wave lasing. The individual CQDs exhibit an ultranarrow single-dot linewidth, and we successfully propagate this into the ensemble of CQDs.