Accommodation is the process of adjusting the eye's optical power so as to focus at different distances. Uncorrected refractive error and/or functional presbyopia mean that sharp focus may not be achievable for some distances, so observers experience sustained defocus. Here, we identify a problem with current models of accommodative control: They predict excessive internal responses to stimuli outside accommodative range, leading to unrealistic adaptation effects. Specifically, after prolonged exposure to stimuli outside range, current models predict long latencies in the accommodative response to stimuli within range, as well as unrealistic dynamics and amplitudes of accommodative vergence innervation driven by the accommodative neural controller. These behaviors are not observed empirically. To solve this issue, we propose that the input to blur-driven accommodation is not retinal defocus, but correctable defocus. Predictive models of accommodative control already estimate demand from sensed defocus, using a realistic "virtual plant" to estimate accommodation. Correctable defocus can be obtained by restricting this demand to values physically attainable by the eye. If we further postulate that correctable defocus is computed using an idealized virtual plant that retains a young accommodative range, we can explain why accommodative-convergence responses are observed for stimuli that are too near-but not too far-to focus on. We model cycloplegia as a change in gain, and postulate a form of neural myopia to explain the additional relaxation of accommodation often seen with cycloplegia. This model produces plausible predictions for the accommodative response and accommodative convergence signal in a wide range of clinically relevant situations.