Since its first demonstration almost two decades ago, the concept of the thin-disk laser has proven its excellent power scaling properties, enabling output powers in the multi-kW-range at decent beam quality. However, power scalability in fundamental-mode operation is limited by severe diffraction losses arising from thermally induced aspherical wavefront distortions in the pumped laser crystal. In order to compensate for these wavefront distortions, we have developed a deformable mirror concept based on pneumatic actuation, providing a step-like surface deformation with adaptable magnitude. Using one of these mirrors, we have achieved output powers as high as 815 W at nearly diffraction-limited beam quality (M2<1.4) from a single disk, which is--to the best of the authors' knowledge-the highest output power at this beam quality demonstrated so far.