With a view to the next generation of large space telescopes, we investigate guide-starfree, image-based aberration correction using a unimorph deformable mirror in a plane conjugate to the primary mirror.We designed and built a high-resolution imaging testbed to evaluate control algorithms. In this paper we use an algorithm based on the heuristic hill climbing technique and compare the correction in three different domains, namely the voltage domain, the domain of the Zernike modes, and the domain of the singular modes of the deformable mirror. Through our systematic experimental study, we found that successive control in two domains effectively counteracts uncompensated hysteresis of the deformable mirror. © 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement.