Here is a possible solution for overtime in the NFL:
For regular season games, the overtime, all 10 minutes of it, would be played. If, at the end of those 10 minutes, the score is still tied, the game ends in a tie.
For postseason games, the first overtime would be mandatory, all 15 minutes of it. But, the difference between that and a regular season game is that, if the game is still tied after those 15 minutes, the game goes into a second overtime, BUT, it then becomes sudden death....next score wins.