We study the voluntary revelation of private information in a labor-market experiment where workers can reveal their productivity at a cost. While rational revelation improves a worker's payoff, it imposes a negative externality on others and may trigger further revelation. Such unraveling can be observed frequently in our data although less often than predicted. Equilibrium play is more likely when subjects are predicted to conceal their productivity than when they should reveal. This tendency of under-revelation, especially of low-productivity workers, is consistent with the level-k model. A loaded frame where the private information concerns the workers' health status leads to less revelation than a neutral frame.