Markets sometimes unravel, with offers becoming inefficiently early. Often this is attributed to competition arising from an imbalance of demand and supply, typically excess demand for workers. However this presents a puzzle, since unraveling can only occur when firms are willing to make early offers and workers are willing to accept them. We present a model and experiment in which workers' quality becomes known only in the late part of the market. However, in equilibrium, matching can occur (inefficiently) early only when there is comparable demand and supply: a surplus of applicants, but a shortage of high quality applicants.