Speaking of which, do you prefer one over the other? I've seen photos of chains used different ways, including through the mouth. The anti-rearing bits just had a ring in the same place as the halter ring, so you'd clip them together with the lead.
Some reference images, in case you don't know quite what I'm talking about.
Chain through the mouth.
Anti-rearing bit (sometimes with a head strap instead of clips).
Under chin, from the cheek.
Over the nose. Most common arrangement?