The drift diffusion model (DDM) provides an excellent account of decisions and response times. It also features the optimal property of tracking the difference in evidence between two options. However, the DDM struggles to account for human confidence reports, because responses are triggered when the difference in evidence reaches a set value, suggesting confidence in all decisions should be equal. Previously considered extensions to the DDM fall short of providing an adequate quantitative account of confidence. Possibly because of this, much confidence research has used non-normative models of the decision mechanism. Motivated by the idea that perceptual decision-making will reflect optimal computation, we consider 9 variants of the DDM. Motivated by the idea that the brain will not duplicate the representation of evidence, in all model variants confidence is read out from the decision mechanism. We compare the models to benchmark results, and make 4 qualitative predictions which we verify in a preregistered study. Modelling confidence on a trial-by-trial basis, we find that a subset of model variants provide an excellent account of the precise quantitative effects observed in confidence data. Specifically, models in which confidence reflects a miscalibrated Bayesian readout perform best. These results support the claim that confidence is based on the decision mechanism, which is itself optimal. Therefore, there is no need to abandon the idea that the implementation of perceptual decision-making will reflect optimal computation.