We study the effects of overlapping identities on wage gaps, focusing on the intersectional effects of gender and race in the US. The extant theoretical and empirical literature argues that this overlap should cause intersectional discrimination, i.e., multiply marginalised groups suffer from a unique penalty in addition to the individual wage gaps they face. By contrast, we find that White men are uniquely privileged compared to all other groups but that Black women do not face a unique intersectional wage penalty compared to all others, challenging previous findings. We dub this phenomenon “excessive White male privilege” and show how it may bias commonly used estimators for intersectional wage discrimination. Recognising and addressing this privilege is essential for dismantling systemic inequality and hence provides a novel tool for the intersectionality studies as well as policy aimed at a more equitable society.