Is there a particular problem that you're having with the "checks, captures, threats" methodology, or do you just feel that it takes too long for a game situation?
If you're looking for an alternative method, I think it would have to start with "which pieces are hanging?" and "which pieces are insufficiently defended (defended only as many times as they are attacked)?" That will clue you in on which enemy pieces are the most vulnerable to tactics, so you can look for a way to attack them with tempo, involve them in a double attack, chase away their defender, etc. You should also pay attention to pieces that are guarded by other pieces rather than pawns, as a defending piece is subject to being overloaded or removal of the guard tactics.
You could also look into some of Heisman's "Seeds of Tactical Destruction" from Novice Nook #5. Chess Cafe recently put their articles behind a paywall, but you can download the free Novice Nooks here:
http://www.chess.com/download/view/dan-heisman-novice-nook-1-100
http://www.chess.com/download/view/dan-heisman-novice-nook-101-143
I don't know if you've seen this already, but if you're looking for a good resource on tactics, try the web version of Predator at the Chessboard. I'm not sure it has exactly what you're looking for, but it's a pretty thorough review of tactics, so it definitely won't hurt.
Ok. Tactics are really starting to $#%@ me off. I need a good, reliable thought process for dealing with tactics. I've seen Dan Heisman's thoughts on thought process but they are WAY too long. There HAS to be a way to develop a thought process which finds all, or at least most, Forks, Skewers, Discoveries, and Pins, that is short. Checks, Captures, and Threats isn't working so I need something else. some form of redundancy.
What are some of your thought processes.
Thanks in advance