Research suggests that accessible coarse‐grain (i.e. general) information is sometimes under‐reported in memory accounts. In two experiments, socially motivating conditions were manipulated to determine whether, and under what contexts, coarse‐grain information is avoided because eyewitnesses are motivated to be specific and willing to risk accuracy. In Experiment 1, response privacy (private, public) and audience (high authority, low authority) were manipulated. Response privacy and penalty for inaccurate reporting (penalty, no penalty) were manipulated in Experiment 2. Across both experiments, eyewitnesses' confidence estimation (i.e. monitoring) was effective, suggesting that coarse‐grain information is under‐reported through poor decision making (i.e. control). Eyewitnesses avoided coarse‐grain information because they sometimes displayed a bias towards reporting fine‐grain information. This bias was more apparent, and coarse‐grain information avoiding more likely, when the perceived consequences for reporting were minimal (i.e. when in private in Experiment 1 and when no penalty for inaccuracy was imposed in Experiment 2). Copyright © 2016 John Wiley & Sons, Ltd.