I just came across this video of the Four Freshmen performing with a backup group of five trombones (Bernie Robier, Doug Elliott, John Jensen, Jay Gibble and Milton Aldana) plus rhythm section. The first soloist, John Jensen, starts playing about 1:49. While his placement looks pretty close to center, the other two trombone soloists, Jay Gibble (starts about 2:26) and Doug Elliott (starts about 3:02) both clearly have mouthpiece placements that are off-center. Take a look.
There are many reasons why a brass musician might place the mouthpiece best off center, and you can see Doug Elliott is quite far off center. Doug has been one of my teachers (the embouchure descriptions I prefer to use are the ones he taught to me) and he sometimes shows that he can play quite well with a centered mouthpiece placement or even a placement off to the other side. However, it obviously works best for him well off on the left side of his lips when he does this demonstration. If you check out Doug’s solo on the above video there’s no question he can get around a very wide range with that precise mouthpiece placement.
What I find interesting about Doug’s placement is that there is really no noticeable anatomical feature I can spot that would indicate why an off center placement would work so much better with him. The story of how he discovered this placement is interesting too. He told me he was playing in a group with very little room to move around (I think it was in an orchestra pit) and in order to watch the conductor and read the music he had to point his bell to the left. He accidentally ended up placing his mouthpiece on the left side of his lips and discovered how much stronger it was for him.
There are some teachers and players I know who make a big deal out of putting the mouthpiece centered on the lips (horizontally, at least), feeling that this is always best for most players. However, when I look closely at different brass players I’ve found that an awful lot of players play at least just a bit off center, and some obviously play best far off to one side. As another example, trumpet player Randy Brecker once told me the reason he places his mouthpiece off to one side is because he has a protruding tooth that has a sharp edge, so he places just to the side of it and it works perfectly well.
Sometimes it’s not obvious that an off center placement will work best for a particular player until he or she tries it, so give it a shot next time you think of it and see what happens. And if you’re one of those players who is constantly trying to get your placement centered and finding it wants to drift to one side, just place your mouthpiece where it wants to work best and quit worrying about what it looks like.