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The control comes from the gut, not the embouchure.

I believe most of the anti-cheek-puffing speech of which you speak is to keep kids from having Satchmo like puffage that does put too much pressure on the face, and can ultimately b detrimental to a players health. I find when i play in the lower register my cheeks don't puff so much as 'expand a little' I figure this comes from a looser emboucure, and lower jaw, and I've found no problem with it. I would suggest that until a beginner can use their abdominals and lungs properly for air support, that the cheeks should not puff at all.

I have a slight overbite. I cannot let my cheeks puff, because when I do I lose all control over my bottom lip, the top lip gets strained, and my tone goes out the window, as well as all my endurance and I subconsciously start "smiling," meaning stretching the embouchure muscles instead of keeping them firm.

As I was taught, when you go lower, drop your jaw. This counteracts the puffiness syndrome by coincidence.

It really can't be avoided in the extreme low register, especially when you really open up (Wagner, etc.) As a pedagogical question, though, I have always found out more helpful to show students what to do, vs. what not to do. If you teach the proper set and the principles of how to adjust for register and dynamics while keeping the airflow as the primary driver of the sound, you should be OK. This only changes if the player has been at it for several years, still puffs in the "money" register, and sounds like <insert>. The solution is still the same, but you will work for your fee.

I said "sometimes" the correct answer wasn't there. The cheeks and everything else are very relaxed; so there will be a slight amount of puffing depending on the back pressure of the horn. So my real answer is: It depends.

(along with 42 being the universal answer to everything)

SplatterTone wrote:
(along with 42 being the universal answer to everything)

indeed...
Especially considering that the freak jury is 'Mostly Harmless"

I don't think you can always avoid it. The determining factor is not what the cheeks are doing, but what the corners of the mouth are doing. You'll find that with advanced players, even though their cheeks might puff out in any register, their corners are still controlled. Keeping control of the corners is everything in an embouchure...tonal quality, intonation, endurance, flexibility, really the whole gamut. Give up control of the corners and everything else suffers and is more difficult to accomplish. Try multiple tongueing without keeping the corners in place.

Controlled does not = tight or pinched.