Numerous coronagraph designs for high-contrast imaging in space have been proposed, differentiated by various performance metrics, such as throughput, inner working angle, bandwidth, ease of implementation (a surrogate for cost), sensitivity, and robustness. In all cases, the performance of the coronagraph is limited by wavefront aberrations in the system, necessitating a deformable mirror (DM) wavefront control system. Traditionally, coronagraphs are designed to achieve the targeted contrast assuming perfect optics, then combined with the controller to correct aberrations in a small dark hole reachable by the DMs. This paper shows how all coronagraphs adjust amplitude and are thus limited by amplitude errors. We propose a unified design approach where the coronagraph is only designed to achieve contrast to the level determined by the amplitude error and in a dark hole consistent with the wavefront controller. The deformable mirrors are then used with the already existing algorithms to generate the remainder of the dark hole. We show new shaped pupil designs with much increased throughput and smaller inner working angles consistent with this approach. These new designs can also be used with on-axis and segmented telescopes.