Why do women hit the glass ceiling? Women are hired, but then fail to rise through the ranks. We propose a novel explanation for this pattern, namely preference- and belief-free discrimination. In our setting, an employer can increase effort by inducing differential value distributions for a promotion across workers, who compete for the promotion by exerting effort. Initially, workers possess the same distribution of valuations. Introducing inequality between workers makes them more recognisable, reducing their information rent, which in turn increases effort. However, higher inequality reduces competition. If value is re-distributed, the reduction in information rent outweighs the loss in competitiveness, making discrimination between workers optimal.