We started to use the Monrad system:
https://rankedin.ladesk.com/043159-2152--Monrad
https://en.wikipedia.org/wiki/Swiss-system_tournament
We are organizing a monthly tournament valid for ELO rating of the United States Chess Federation (USCF). The rating of our players is in the range 2000-400. We play a maximum of 3 rounds. Usually, we have between 8 and 16 players. This is an amateur tournament, in other words, no cash prizes. Players who achieve 3 points get a gold medal, 2 points a silver medal, and 1 point a bronze medal. We found that the classic Swiss system produces that a big percentage of the lower players retired from chess.
In my experience, in a game with a rating difference of 400 points, the lower rating player has a minimum of 90% chance to lose. In general, that will occur.
For that reason, we started to use the Monrad system.
If the highest rating is number 1, and the lowest rating is number 16. Without considering colors, the Swiss system produces 1-5, 2-6, 3-7, 4-8. But the Monrad system 1-2, 3-4, 5-6, 7-8.
The Monrad system is great because our main goal is to have a pairing with the smallest ELO rating difference possible. However, is it legal to use it for an USCF open tournament? It will be announced in advance. So, the players will know about it before to register. Our tournaments do not offer cash prices.
My main interest is in USCF. However, I would also like to know if it is legal for the International Chess Federation (FIDE).
As far as I know, the tournament organizer can use any system, if it is announced in advance and if it is NOT a national or international championship with established rules that the tournament organizer needs to follow.
Thank you for everything!