Humans typically make near-optimal sensorimotor judgements but show systematic biases when making more cognitive judgements. Here we test the hypothesis that, while humans are sensitive to the noise present during early sensory encoding, the “optimality gap” arises because they are blind to noise introduced by later cognitive integration of variable or discordant pieces of information. In six psychophysical experiments, human observers judged the average orientation of an array of contrast gratings. We varied the stimulus contrast (encoding noise) and orientation variability (integration noise) of the array. Participants adapted near-optimally to changes in encoding noise, but, under increased integration noise, displayed a range of suboptimal behaviours: they ignored stimulus base rates, reported excessive confidence in their choices, and refrained from opting out of objectively difficult trials. These overconfident behaviours were captured by a Bayesian model blind to integration noise. Our study provides a computationally grounded explanation of human suboptimal cognitive inference.