I am fascinated by old customs and I think some of them might be good to bring back. Dueling was accepted in in Europe many years ago and was practiced in the United States till the 1840's until it became frowned upon.
Usually when one party felt they had exhausted all other means to settle an issue they would challenge the other party in a public place. The other party had the option to drop the issue and apologize or pay restitution or accept the duel.
I think this is a idea which we seriously need to revisit, think of all the money we could save. It would stop a lot of frivolous law suits, not many people would be willing to risk death or serious injury over a fake claim. It would certainly make most people want to do the right thing instead of trying to wrangle out through legal loopholes. For example, you have a minor auto accident, it is your fault and you or you insurance company pays for the damage however the other party claims they cant work or function due to back pain, nightmares, whiplash etc. You know it is a sham because it was a bump in a parking lot for instance so you challenge them to a duel. They now have a choice either back down and publicly admit they were lying or face a duel, my bet is 99.99 % of the time they would back down. Even if you had professional duelers which you could hire to represent you they would cost a fortune and regardless of which side won the issue would be settled and no further payment would be required so another reason most would back down before it went that far.
Or lets say for example someone owes you money and they fail to pay, if challenged to a public duel almost all offenders would pay up to end the issue, if not you would get the opportunity to extract your pound of flesh, win or loose the issue would be over.
Usually in any argument between two parties one of them knows in their heart they are lying so for this reason I think this would be a wonderful system, it would save a ton of money in law fees, insurance payments, jail over crowding and would be a excellent way to keep people honest.