To further this question (and maybe this deserves to be in the Multiplayer forum), is it possible for the game to *remain* private when you reload it. Me and my friends are trying to play multiplayer games of civ once a week, and time constraints obviously mean saving and reloading the following week.
However, we've found that if a player drops for whatever reason (generally, not enjoying the game), there's no way to stop random other people trying to join the game. The private setting works fine when you create a new game, but there's no way to keep it private when you load a save (yes, I've tried ticking the private game box before loading, it doesn't work).