The present study examines the effect of a supervisor (leadership) position on a father’s time spent on child care (child care involvement). Drawing on time use and work–family research, it adapts the "stress of higher status" hypothesis to child care involvement and explicates the underlying mechanism. The proposed moderated mediation model posits that (1) a leadership position means longer work hours, which explains the lower child care involvement, and that (2) this process depends on the possibility to choose when to start and quit work (flextime), which weakens the work–family border. A Swiss sample (n = 2,820) of tertiary-educated, employed fathers from couple households is used to conduct the analysis. The results provide evidence for both (1) and (2), although, contrary to expectations, flextime does not mean longer work hours for leaders. The issue of child care involvement by fathers in leadership positions has wider relevance for work–family issues, because they are supervisors and thus shape work environments.