High quality, repeatable point-spread functions are important for science cases like direct exoplanet imaging, high-precision astrometry, and high-resolution spectroscopy of exoplanets. For such demanding applications, the initial on-sky point-spread function delivered by the adaptive optics system can require further optimization to correct unsensed static aberrations and calibration biases. We investigated using the Fast and Furious focal-plane wavefront sensing algorithm as a potential solution. This algorithm uses a simple model of the optical system and focal plane information to measure and correct the point-spread function phase, without using defocused images, meaning it can run concurrently with science. On-sky testing demonstrated significantly improved PSF quality in only a few iterations, with both narrow and broadband filters. These results suggest this algorithm is a useful path forward for creating and maintaining high-quality, repeatable on-sky adaptive optics point-spread functions.