Honestly, the question is how low could you cut the bracket and have it still be exciting. I mean with 16 players, the tournament will have four rounds, right? The top 16, the top 8, the top four (semifinal) , and the top two (final); add an extra round if you're doing double elmination, which I strongly recommend. If you chop that in half, you have only three-four rounds instead of four-five. It's a question of how much suspense you want. It seems kind of strange to me that there are so few people being left out, since they must feel terribly alone, but I am not complaining about the familiar 16 competitor tournament bracket and wonder how it could work otherwise.
One interesting thing you could look into is three person head to heaed instead of two for the first round. Say you take the top twelve teams and put them in groups of three. For each triad, the best time goes into the main bracket, the second into a lower bracket, the third is eliminated. Then you have 8 teams left and 3-4 more rounds (8 players, 4 players, 2 players, then possibly the two brackets face off). That way more teams are excluded, but you tsill get a fairly lengthy tournament bracket.
As for multiperson rounds, if you only have one level per round, then you should have a rule mandating that team members have to alternate or something. If you say that each team member must do 50% of the semifinal, then you will probably have an influx of the strongest member of the team going the first two rounds so as to guarantee a higher final placement. If you require them to alternate, with 2D/3D alternated accordingly, that'll be more indicative of their actual position.