Interesting stuff. I've just done a little reading, and I don't think I'm too worried about the harmonic distortion so much as what might be called, or at least looks like, DC OFFSET. Now maybe it is phase shifting or something else, and I plan on learning more this weekend, but I just found this interesting quote:
"Calling it "Centering" the wave is ambiguous -- perhaps this is something that Adobe should make note of. DC offset is easily diagnosed when there's a low-level signal, such as "open air," and the waveform sits off of the center line. Asymmetry is an entirely different matter, as you've all noted, and is usually caused by close-miking a voice, trumpet, trombone, or saxophone, all of which produce sounds with little puffs of air at the source. Andy & James, somewhere else it was noted that phase-shifting a voice could remove the asymmetry and allow a louder final result."
Now that's two "puffs" of air comments in a row, and all related to horns. Plus, it does look a little more "asymetrical" than strictly "off-center." Hmmm...