Despite well-intentioned efforts, the supply of women into senior management roles has changed little. Radical ideas are apparently needed. This paper is an attempt to suggest one. It is to use a form of random selection of candidates – drawn from a pre-selected and properly qualified pool – to increase the supply of women into management positions. The background rationale is that while most gender studies have focused on the demand side (direct and indirect discrimination), we think about how to improve the supply side, and in particular how to find ways to reduce negative self-stereotypes and stereotype threats. Evidence suggests, for example, that women shy away from competition, and are especially averse to rejection. We argue that a random-draw method would offer women a type of ‘rejection insurance’, lessen the ‘chosen one’ factor associated with leadership, prevent the desire for a ‘safe pair of hands’ (i.e. a man), and foster genuine equality.