I see both Al's and Robin's side of the coin on this one. If a player is playing radically off to one side or another, or is playing with extreme upper or bottom lip, I think that a change to mouthpiece placement should be considered. However, I also agree with Robin in that paying dues in the practice room tends to bring the mouthpiece to where it should naturally be based on jaw, lips and teeth. Having said that, I know one guy who's college instructor tried to move his placement which was off to one side toward the center, and it almost ruined him as a player, and it took him a fair amount of time to rebuild what he'd lost after he moved things back to where they were to begin with. This is a guy who had a big phat sound and screaming range BEFORE the change - why his teacher thought he needed a change is beyond me, although my friend's theory on the matter is that it was done out of jealousy because his teacher didn't have that kind of upper register range. I play off to the left - not radically, but enough that you can see that it's not centered. I play there because that's where my teeth dictate the mouthpiece should be. I have noticed in the last year or so (a fairly new development for me considering almost 30 years on the horn) that if I consciously shift the mouthpiece ever so slightly toward the center that I have much better endurance and strength to my chops over the course of a gig with the party band. I'm not talking about a big shift though - just enough that I know that I've moved toward the center. I'm not quite sure how I came to that realization though - I just know that if I consciously move slightly more toward center, it helps. Regarding top/bottom lip positioning, that has also shifted for me over the years, and none of it was done consciously - it was all done in a very natural way and I wasn't even aware it was happening until after it had already happened. When I first started taking off with the trumpet in middle school and high school, I played with the mouthpiece really high - we're talking 3/4ths top, 1/4th bottom. As I got into the Army band program and started playing a lot more, and the focus of my playing shifted toward needing a bigger, more open sound, (2nd book in the quintet, 2/3rd parts in the concert band and 3rd/4th books in the big band) my mouthpiece placement naturally shifted downward to where I had a 2/3rds bottom, 1/3rd top placement. After I got out of the Army and my playing styles shifted to a brighter, more commercial sound in the Latin and party bands, and I started using a smaller mouthpiece, that vertical placement shifted again and now I play about 2/3rds upper, 1/3rd lower. (maybe not quite that much, but it's definitely more on the top lip than the bottom) I didn't consciously shift any of that.