We have constructed a high-speed image stabilization system, BESSEL, that is capable of performing wavefront correction at a rate exceeding 1 kHz. BESSEL achieved on-sky Strehl ratios of 98-99% at 800 nm as we approached the inner scale of atmospheric turbulence when the refractor telescope aperture was stopped down to 25.4 mm (̃r0/2). This is better than expected from Kolmogorov theory, indicating that at D ̃r0/2 we are within the inner scale of turbulence. Utilizing high Strehls and the technique of roll subtraction enabled BESSEL to resolve the binary, ADS 10418AB, with separation of only 0.71 ?/D and a delta magnitude of ̃3 mags at 800 nm. BESSEL's capability to produce high Strehls ratios means that the instrument can be used to test the performance of interference/phase coronagraphs on-sky for the first time. Integrated with an optical vortex coronagraph, BESSEL is capable of nulling the first airy ring of Betelgeuse by more then a factor of ten.