Academic debate on the strategic importance of women corporate directors is widely recognized and still open. However, most corporate boards have only one woman director or a small minority of women directors. Therefore they can still be considered as tokens. This article addresses the following question: does an increased number of women corporate boards result in a build up of critical mass that substantially contributes to firm innovation? The aim is to test if ‘at least three women’ could constitute the (...) desired critical mass by identifying different minorities of women directors (one woman, two women and at least three women). Tests are conducted on a sample of 317 Norwegian firms. The results suggest that attaining critical mass – going from one or two women (a few tokens) to at least three women (consistent minority) – makes it possible to enhance the level of firm innovation. Moreover, the results show that the relationship between the critical mass of women directors and the level of firm innovation is mediated by board strategic tasks. Implications for both theory and practice, and future research directions are discussed. (shrink)