We present high-performance megahertz micromechanical oscillators based on freestanding epitaxial AlxGa1−xAs distributed Bragg reflectors. Compared with dielectric reflectors, the low mechanical loss of the monocrystalline heterostructure gives rise to significant improvements in the achievable mechanical quality factor Q while simultaneously exhibiting near unity reflectivity. Experimental characterization yields an optical reflectivity exceeding 99.98% and mechanical quality factors up to 20 000 at 4 K. This materials system is not only an interesting candidate for optical coatings with ultralow thermal noise, but also provides a promising path towards quantum optical control of massive micromechanical mirrors [1].High-quality Bragg mirrors with small mechanical dissipation have generated recent interest due to their versatile use in both fundamental and applied sciences. Specifically, mechanical dissipation in optical coatings is known to limit the performance of high-finesse cavity applications, in particular gravitational wave interferometry [2] and laser frequency stabilization for optical clocks [3], because of residual phase noise, also referred to as coating thermal noise [4]. On the other hand, microstructures of high mechanical and optical quality have become a leading candidate to achieve quantum optical control of mechanical systems. One specific goal in this emerging field of quantum optomechanics is to combine the concepts of cavity quantum optics with radiation-pressure coupling to generate and detect quantum states of massive mechanical systems such as the quantum ground state [5,6,7] or even entangled quantum states [8,9,10]. The recent demonstrations of cavity-assisted laser-cooling of mechanical modes [11,12,13,14] can be considered an important milestone in this direction.Most of these schemes rely crucially on mechanical structures that combine both high optical reflectivity R and low mechanical dissipation, i.e. a high quality factor Q of the mechanical mode of interest. In addition, entering the quantum regime will require operation in the so-called sideband-limited regime [5,6,7], in which the cavity bandwidth of the optomechanical device is much smaller than the mechanical resonance frequency. [18], the mechanical quality factor of free-standing DBRs is limited to below 3000 due to internal losses in the Ta 2 O 5 layers [19]. It is interesting to note that the low Q-value obtained with these devices is consistent with the coating loss angles observed in the LIGO studies of gravitational wave detector coatings of the same material [2,4]. On the other hand, the use of SiO 2 /TiO 2 -based DBRs has led to the demonstration of mechanical quality factors approaching 10 000 at room temperature [12]; there, however, optical absorption in TiO 2 at 1064 nm both limits the reflectivity and results in residual photothermal effects.The concept outlined here seeks to improve upon these previous works by fabricating the oscillator directly from a single-crystal Bragg reflector. In particular, the use...