One of the intellectual movements in chess over the last fifteen years has been the attempt to transform sudden-death into an amazingly lifelike imitation of "real" chess, with repeated time controls. This has mostly involved the use of high-tech digital clocks. There are essentially three flavors.
1) "Time-delay," standard in the U.S. When the opponent stops his clock and starts yours, your clock does not begin ticking down for a specified number of seconds (typically five).
2) "Bronstein," named for the late GM who suggested it back in the early 1970s. (Also known as "non-cumulative addback.") When the opponent stops his clock and starts yours, a specified number of seconds is added to your time, to a maximum of the time you had when you started your last move. Example: You have 20 seconds left. You think for six seconds and make your move, leaving you with 14. When your opponent moves, your clock immediately jumps back to 19. Example 2: Same as before, except that you use only three seconds, leaving you with 17. When your opponent moves, your clock jumps back to 20 (not 22). Mathematically this is more or less identical to time delay, but it is less used, probably because it's harder to explain.
3) "Fischer," also known as "increment" or "cumulative addback." The standard adopted by FIDE, most often in the form of game in 90 with an extra 30 seconds for each move. It operates in the same manner as Bronstein, except that there is no limit to the amount of time you can accumulate. Make a lot of moves quickly, and you can easily go from one second to five minutes.
The "Fischer" mode has been fairly rare in the U.S., though it has been used for the U.S. Championship and for some title-norm round-robins. These operated quite well by simply using the FIDE rules. Recently, however, the USCF Rules Committee decided that we really, really needed new rules of our own. (The committee chairman is apparently a big fan of Fischer increment, and wants to encourage its adoption.) Most of the "new" rules voted on at the recent Delegates' Meeting were taken straight from the FIDE Handbook.
However, there is one oddity. What happens if both flags are down? Under FIDE procedure, this is very unlikely to arise, since the arbiter is supposed to watch the game and call the flag. That is probably not going to happen in American Swiss tournaments, so the Rules Committee chairman came up with a novel interpretation: Fischer increment is "not really" sudden death. Instead, once your original time is used up, it's "really" unlimited repeating time controls of 30 seconds/move. Thus, under the new USCF rule, if both flags are down, the game is not drawn (as it would be in sudden-death). Rather, the clocks must be reset with zero time plus 30 second addback for each player and the game continued. If you think resetting the clocks that way is going to be a pain, you're right.
A simple solution, until the next time the USCF tinkers with the rules: If you must use Fischer increment, announce in advace that you are using FIDE rules. If you don't have enough TDs to watch all the games, well, you probably shouldn't be using increment to begin with.