Tournament Joust is a free print and play game with some really good looking jousting mechanics. It has paper knights, but you’ll want to swap in your own miniatures.
Games Workshop’s Lord of the Rings rules set has turned out to be very flexible, spawning several commercial sets, such as Legends of the Old West and Legends of the High Seas and innumerable fan variants. Legends of the Feudal Times is a set of feudal skirmish rules originally published in the French language magazine Vae Victis. The English translation is here.
Standard Wargame Rules For Ancient and Medieval Warfare is an alternative to DBM with the same basing. The authors write:
The designer team includes both extremes of wargamers: dedicated tournament players as well as those who prefer historical re-fights. These rules aim to satisfy these both sides of the wargaming hobby. We wanted to write a set of rules that allows playing realistic and interesting re-fights of historical battles. Furthermore, we have spent much time to make the rules as exact as possible, so that they are also suitable for tournament play. Once both players know the rules, there should be no need for an umpire or for long rules discussions during the game.
One aim was also to design a rule set that is “easy to learn but difficult to master”. This means that you can learn the rules relatively quickly, but will probably need several games, before finding the optimal tactic for your army. Also, there are no “super troops”. Each troop type has certain strengths and weaknesses that you will need to learn.
A Great Victory is a set of free wargames rules for miniature wargames set in the pregunpowder era.
God Will Know His Own is a set of free wargames rules for “Knight and Crossbow era Wargame Rules 1096-1590(or 1789) then into the horse and Musket era.”