The paper explores the impact of the gender composition of Boards of Directors on gender diversity and earnings gaps among executive management using administrative data on all Danish private sector firms from 1995 to 2018. We find that it is not the quantity of women directors but the quality of the women entering the board that matters in generating positive spillovers on the gender gaps within the firms. Quality is viewed as the power, conceptualized as the possible influence in the boardroom, and operationalized as the position and board experience of the directors. A way of channeling power is also through the director's networks. Powerful women directors increase spillovers, while male directors have a negative impact. However, male directors' connections to females positively decrease the gender gaps. Interestingly, the spillovers are not large enough to generate a sustained change in the gender composition of the executive board, mainly because women executives exit to a larger extent than men.