This paper reports on novel approaches developed for plasma-assisted molecular beam epitaxy of Al-rich AlGaN epilayers and quantum well heterostructures on c-sapphire, which allowed us to fabricate low-threshold optically-pumped separate confinement heterostructure lasers emitting in the mid-UV spectral range (258–290 nm) with the threshold power density below 600 kW cm−2. The optimum buffer structure has been developed which provides lowering the near-surface threading dislocation density down to 1.5 × 108 and 3 × 109 cm−2 for screw and edge types, respectively, and improving the surface morphology (rms < 0.7 nm at the area of 3 × 3 μm−2). It comprises the high-temperature (780 °C) migration enhanced epitaxy growth of a (30–70) nm thick AlN nucleation layer on c-Al2O3, followed by a 2 μm thick AlN buffer grown under the metal-rich conditions in the Al-flux modulation mode and containing several (up to 6) ultra-thin (∼3 nm) GaN interlayers grown at N-rich conditions. Proper strain engineering in AlGaN single quantum well heterostructure grown atop of the AlN buffer layer enables one to preserve dominant TE polarization of both spontaneous and stimulated emission even at shortest obtained wavelength (258 nm). The threshold power density of stimulated emission as low as 150 kW cm−2 at 289 nm for a single quantum well laser structure has been demonstrated.