A head-mounted device may have a main housing containing displays that display images to eye boxes for a user when the head-mounted device is worn by the user. The head-mounted device may include a light-shielding structure coupled to the main housing and configured to rest on the nasal region of the user. The light-shielding structure may include rigid members, flexible members, and/or fabric members. The light-shielding structure may conform to the facial features of the user around the nasal region to block environmental light from entering the eye boxes when the head-mounted device is worn by the user.