The comparison between conscious and unconscious perception is a cornerstone of consciousness science. However, most studies reporting above-chance discrimination of unseen stimuli do not control for criterion biases when assessing awareness. We tested whether observers can discriminate subjectively invisible offsets of Vernier stimuli when visibility is probed using a bias-free task. To reduce visibility, stimuli were either backward masked or presented for very brief durations (1–3 milliseconds) using a modern-day Tachistoscope. We found some behavioral indicators of perception without awareness, and yet, no conclusive evidence thereof. To seek more decisive proof, we simulated a series of Bayesian observer models, including some that produce visibility judgements alongside type-1 judgements. Our data are best accounted for by observers with slightly suboptimal conscious access to sensory evidence. Overall, the stimuli and visibility manipulations employed here induced mild instances of blindsight-like behavior, making them attractive candidates for future investigation of this phenomenon.