We study the voluntary revelation of private, personal information in a labor-market experiment with a lemons structure where workers can reveal their productivity at a cost. While rational revelation improves a worker's payout, it imposes a negative externality on others and may trigger further unraveling. Our data suggest that subjects reveal their productivity less frequently than predicted in equilibrium. A loaded frame emphasizing personal information about workers' health leads to even less revelation. We show that three canonical behavioral models all predict too little rather than too much revelation: level-k reasoning, quantal-response equilibrium, and to a lesser extent inequality aversion.