The problem with a single elimination bracket is that the best team usually does not win, just look at the NCAA basketball tournament.  I would say do a double elimination bracket, but that would be way too many games to play.  

If you recall, the format used in 1980 games was that the top 2 teams emerged from each pool and played both teams from the other pool (there were only 2 pools of 5 teams.  The combined record at the end decided the gold medal.  If team USA had lost to Finland, they would not even have gotten the bronze medal.  As it turned out, the Soviet team won the silver even though they lost to team USA.

The Olympic committee needs to get 24 teams down to 3 in 14 days.  The current format works for that.  A team can avenge a loss in pool play and still get a gold medal.