I'm just banging out some simple combat rules for jousting, for use in duels and tournaments. I'd welcome any comment or suggestions, as it's still in the tweaking stage.

Rules of Formal Jousting:

Note that this combat system does not apply to ordinary mounted combat: It is specifically for a formal joust, where the riders are following the jousting rules and conventions in an honorable tournament or duel. Each rider waits for a signal or consensus (both riders lower their lances to attack position before proceeding) before charging forward on a trajectory to pass close by, attacking with lances, attempting to knock the opposing rider off their horse. In a sports tournament, the first to dismount his opponent three times is proclaimed the victor. In a duel, the victor is the one who survives, or accepts his opponent's surrender.

No damage is done during tournament/friendly/sports jousts (except on a crit fail) due to practice lances being enchanted or designed to do no harm. On a crit fail, roll any other die: Odd numbers, the jouster managed to somehow clumsily unseat himself. Evens, the jouster struck their opponent or the opponent's mount for actual critical lance damage, disqualifying himself from the tournament and possibly making a deadly enemy. In addition, friendly jousts bar 'extra' attacks, such as whacking your opponent with your shield or allowing your mount to crash into or otherwise take aggressive action against the opponent. These are common but disreputable tactics in serious fights, but considered fouls in friendly sporting events, and repeated infractions may lead to a poor reputation and possibly being barred from future tournaments..

Initiative is rolled for each round, to determine which lance strikes first.

Both jousters charge forward, and roll to hit. When hit, a rider must make a strength saving throw DC the strength of the opposing player.  (Advantage on the roll for those with the Mounted Combatant feat.) If the save is failed, the rider is dismounted and knocked prone.

If a rider is dismounted by the attack with initiative, his own attack is an automatic miss UNLESS they have rolled a critical hit (in which case the second rider also gets a hit, making it possible that both riders are dismounted simultaneously) OR if they have the Mounted Combatant feat (in which case their attack is treated normally, again making it possible both riders have dismounted each other.)

Against a critical hit, the save vs being dismounted is made with disadvantage.

Charging Damage: If hit, charging damage is added to the attacker's damage inflicted, equal to the strength bonus of the mount.

Once a rider is dismounted, if their mount is still available, they will have a turn in which to re-mount before the opponent can slow and turn their mount for the next pass.  If the dismounted rider can not immediately remount, it is etiquette for the victorious rider either to give them more time to remount, or dismount to continue the battle on foot. Continuing to attack a dismounted opponent from horseback is considered cheating, and a dishonorable act of treachery and cowardice, and will remove the rider's eligibility for any sort of formal dueling henceforth. On the other hand, if the dismounted rider attacks the still-mounted rider before or while they dismount, the rider is free to carry on fighting from the saddle with no stigma attached.

ALTERATE MOVE: Rather than striking the opponent with the point of the lance, a second option is to turn the lance and strike them with the side. The advantages and disadvantages of this attack: 1. Sideswiping automatically loses initiative, unless the opponent is using the same tactic. 2. Rider gains advantage to hit, but damage is halved. 3. In terms of etiquette, it is considered a cheap shot.

Animal handling: If a rider is on an unfamiliar or untrained mount, a DC10 animal handling check must be made for each pass. Critical failure may lead to the mount turning tail and running (causing loss of prestige and embarrassment), blundering into the opposing mount (sports foul), or taking some other action that prevents the rider attacking or lowers their defenses. Another animal handling check should also be made for an unfamiliar or untrained mount any time the rider is dismounted: on failure, the mount runs off and is not available to remount until/unless it is caught.

have you bounced yours off of legacy/homebrew? I've found that looking at legacy rules and other homebrew rules helps me find holes / balance issues / potential improvements in my own stuff, regardless if I use any of it or not.  I would recommend reading Dragon issue #299 and Complete Warrior.  There's also two homebrews you might find useful: Tournaments, Fairs, and Taverns (pathfinder) and Cavalier's Handbook (3.5).   The numbers will obviously change but many of the core balancing issues could very well help / confirm your own stuff as well as give you new ideas.

i'd have at least a little bit of real bludgeoning damage. 

I personally don't like the remount rules. Its a joust, the point is given to the one that dismounts the other...period (imo). 

i think the animal handling rules also could be tweaked...i'd say if the animal handling check fails, they just get disadvantage on the attack role. also no 'runs off' as i'm guessing its usually in a ring / jousting area (plus the animal isn't getting attacked).  I can't really think of many scenarios where someone would joust with an untrained mount...you probably couldn't, DC 20 to the animal handling check at the very best....but probably more like 25-30.

Also, I believe there are no critical failures on ability checks.