How can choice, confidence, and response times be modeled simultaneously? Here, we propose the new dynamical weighted evidence and visibility (dynWEV) model, an extension of the drift-diffusion model of decision-making, to account for choices, reaction times, and confidence simultaneously. The decision process in a binary perceptual task is described as a Wiener process accumulating sensory evidence about the choice options bounded by two constant thresholds. To account for confidence judgments, we assume a period of postdecisional accumulation of sensory evidence and parallel accumulation of information about the reliability of the present stimulus. We examined model fits in two experiments, a motion discrimination task with random dot kinematograms and a postmasked orientation discrimination task. A comparison between the dynWEV model, two-stage dynamical signal detection theory, and several versions of race models of decision-making showed that only dynWEV produced acceptable fits of choices, confidence, and reaction time. This finding suggests that confidence judgments depend not only on choice evidence but also on a parallel estimate of stimulus discriminability and postdecisional accumulation of evidence.