Biomechanical studies of concussions have progressed from qualitative observations of head impacts to physical and numerical reconstructions, direct impact measurements, and finite element analyses. Supplementary to a previous study, which investigated maximum principal strain, the current study used a detailed finite element head model to simulate unhelmeted concussion and no-injury head impacts and evaluate the effectiveness of various tissue-level brain injury predictors: strain rate, product of strain and strain rate, cumulative strain damage measure, von Mises stress, and intracranial pressure. Von Mises stress was found to be the most effective predictor of concussion. It was also found that the thalamus and corpus callosum were brain regions with strong associations with concussion. Tentative tolerance limits for tissue-level predictors were proposed in an attempt to broaden the understanding of unhelmeted concussions. For the thalamus, tolerance limits were proposed for a 50% likelihood of concussion: 2.24 kPa, 24.0 s-1, and 2.49 s-1 for von Mises stress, strain rate, and the product of strain and strain rate, respectively. For the corpus callosum, tolerance limits were proposed for a 50% likelihood of concussion: 3.51 kPa, 25.1 s-1, and 2.76 s-1 for von Mises stress, strain rate, and the product of strain and strain rate, respectively.