Despite gains overall, women are still under-represented in leadership positions in science, technology, engineering, and mathematics (STEM) fields. Data in the US suggest around one-quarter of deans and department heads are women; in science this drops to nearly 1 in 20. Part of this problem of under-representation stems from the population pool: only 33% of science and engineering doctorate holders employed in academia are women. Other issues include well-known problems of women's participation in STEM fields: lack of role models, unconscious biases, discrimination, and unwelcoming climates. This paper examines the primary barriers to women's participation in (1) STEM areas and (2) arenas. Examination of the two suggests that women in STEM fields are particularly susceptible to the barriers and biases facing women who wish to move into leadership positions. The similarity in the barriers in these two areas could lead to an effective double jeopardy for women entering STEM leadership. A distinct lack of research in the area of women's leadership in STEM fields suggests that this is a major problem that is not currently understood and not being addressed. (Contains 1 figure.)