Optimal board size is a fundamental question in corporate governance with prior research linking board size to firm complexity, typically measured using coarse proxies. We introduce a text-based approach that applies a complexity lexicon to firms’ annual reports, allowing us to differentiate complexity along distinct dimensions. Complexity terms are strongly associated with board size. Importantly, different dimensions of complexity are associated with different board structures: advisory-oriented complexity is associated with larger boards, while monitoring-oriented complexity is associated with smaller boards. These findings highlight meaningful heterogeneity in complexity and its relation to board size.