Here is a variant played in Auckland, as told by Carl Schnackenberg:

We only have one night period; the rest is day. There is no moderator and players are either mafia (around a third) or citizens (though I guess civilian is a more appropriate label). Once players have drawn their cards, all close their eyes. One preselected player (also with eyes closed) knocks twice. The mafia then open their eyes, look at each other, and close them again. After a reasonable period of time the knocker knocks again and all the players open their eyes. It can be quite fun when one of the mafia has failed to see the others.

The rest of the game is basically a succession of lynchings. Accusations fly, everyone shouts, and when enough general feeling builds up about a person, anyone can call a vote. Voting is by show of hands and if a majority of voting hands are in the air at once, the accusee is killed and has to profess his or her identity. It is very difficult for the mafia, who don't get a rest from lying and tend to have to rely a lot on misled citizens. The dead aren't really supposed to talk and mostly they just sit and watch the game, but often a particularly slighted dead citizen will haunt people constantly accusing them of being mafia and usually noone stops them.

The moderating role of the moderator is quite well served by the general feeling of the group. It may sound a bit unstructured, but it really goes off and has always worked well with new players.