
Safe haven
Upon committing a major crime, the accused one is banned from his home. The family of the one he has done harm to, is responsible for his safe passage to a special town, where "criminals" may dwell without any punishment. Every attempt to take revenge on the accused one are punished by extinction of the family. Whenever the accused one leaves the safe haven again, he is free as a bird (in terms of fair game).
Voice of the majority
When a trial takes place, the accused person and the accuser shall bring all those who support one party to the trial. No witnesses, no evidences, just the number of supporters decides who is right and who is not.
Eye for an eye
Jews might know this principle, whenever one claims that somebody else has done harm to him in any way, twice this harm is done to the accused person. This also holds for the whole family - when a mother loses her son to an accident, two sons of the family of the one who caused this accident are slain in a way, as similar as possible to the accident.
Money makes the world go round
As simple as it is, for every crime, there is a fine. Who pays the fine is as not-guilty as ever before, no matter what crime. Who does not pay the fine (or cannot), loses all he has and ends as slave. Slaves have, of course, no rights and thus, must not commit any "crimes".
Maybe you also have ideas how alternate societies could work?