But TV networks and even arenas don't want playoff style OT - which can be endless - for games in September. Coaches and GMs likely don't want to worry about the prospect of 100+ minute games playing teams like Minnesota either. (The Wild led the NHL last season with 20 games going to the shootout).
So my suggestion starts with something that's already a popular idea and far from original.
Change #1: Three-on-three double OT. (And it starts one minute after the first OT - no flood, no scrape.)
But I have a few additional suggestions that I think help ensure that games are decided BEFORE a shootout (which is a concept even people who don't hate the shootout can get behind).
First off, you need to limit whistles. Tired players, frantic line changes and continuous play makes for exciting hockey (not to mention less "real" time making networks or arena staff impatient). So with that:
Change #2: In 2OT, no icing and no offside (no lines basically)
Change #3: In 2OT, no line changes after any whistle* - puck is dropped as quickly as officials can get set
* If a player is injured they can leave the game entirely (cannot return) and someone can substitute in. On a penalty, the penalized player leaves the ice but no other players may change until after the puck is dropped again.
The idea here is that less whistles equates to more north-south hockey, more turnovers and on-the-fly line changes. More chances for mistakes and mistakes in the NHL typically lead to odd man rushes and highlight reel goals or saves. Referees could also encourage goalies to move the puck if no fore-checker is nearby or face a delay of game penalty. Anything within reason to limit the number of whistles and keep the play moving.
Should that still fail to produce a winning goal, one more rule change on penalty shots in general (and of course applied in the shootout) would prevent things from turning into a Daug and Perry show. (Daugavins-style puck pin or Perry-style lacrosse play.)
Change #4: A player taking a penalty shot cannot touch the puck until after the official whistles it into play (the puck is on the center dot, player outside faceoff circle)
Once the player starts forward to the puck, they cannot stop moving forward. Meaning if someone wants to try pinning or lifting the puck, they risk fumbling the puck and blowing their attempt (similar to a clear break away). That should, for the most part, limit shootout attempts to what players could theoretically try in a game (Google "Phil Bourque breakaway 1990").
Now About Awarding Points
3 points for a win positively horrifies purists and casual fans alike, and for good reason in my opinion. And there are crazier ideas out there: I've seen people suggest half points or systems starting with 5 points for a regulation win etc. My changes here are far from extreme but still motivates teams to do everything they can to settle the game BEFORE the shootout. Teams still get two points for a win in regulation, overtime or double overtime but:
Change #5: Only 1 point for shootout win
Change #6: 0 points if you lose (no matter when)
Put another way, there are no more charity points for "losing slowly" (in OT or SO) and less reward for a team not able to put their opponent away before the shootout. Regulation wins becomes the new tie breaker in the standings rather than ROW (a small motivator to win in regulation).
Without the consolation point for losers, no team will "settle" for OT or a shootout since there's no guaranteed point. Making the last few minutes of regulation pretty wild in a tie game. And the 2OT would get pretty desperate when your best case in a shootout is only a single point.
Perfect? No. I'm sure players and coaches will find creative ways to exploit the rules to try and get a couple of extra points in the standings along the way. But I think this would encourage teams to simply play hard to win games in regulation, or at the very least before the shootout. Of course, had these rules been in place in 2011-2012 teams would have played with different intensity (I hope, since that's the intention of these suggested changes) but here's how the final East standings would have looked with the suggested points system.
The biggest thing here is that Florida falls right out of the playoff picture (Washington now winning the Southeast) with the Lightning taking their spot (and bumping Ottawa up to the 7th seed where we would have had our chance to use all those Obama-Thomas jokes we all planned). Ah what might have been. Note that the 3-2-1 system doesn't impact playoff seeding at all and barely tweaks lottery seeding.
One Last Rule Change...
Since I'm on a roll here (and just because it's a pet peeve of mine):
Change #7: Any player who still has penalty time to serve when 2OT ends is NOT eligible for the shootout.