I can think of at least three ways to "pucker" the lips when blowing a brass instrument. There's probably more actually. Here:
1. Stuff more lip flesh into the mouthpiece. Kind of a crude way to manipulate the chops for better register but perhaps useful in the early stages of high range production.
2. Roll out more lip flesh into the mouthpiece. Similar to number 1 above and probably almost as crude. Again possibly helpful depending upon individual variances.
3. Make the lip flesh THICKER against the mouthpiece. The subject of this thread.
So what does "thicker against the mouthpiece" mean you may ask?
A. Walk over to a mirror or pick up a hand held one.
B. Put your face about a quarter inch away from the glass.
C. Make your lips in the position where you would normally call your setting embouchure.
D. Without moving your head at all PUSH your chops FORWARD closer until they touch the glass.
Also there are probably several ways of accomplishing "D" above and any or all may include some part of 1, 2 and 3 above.
Anyway if you can learn to blow this way (its an easy trick to learn) it ought to add miles to your endurance. You will also unwittingly bring more of your facial muscles into the game. Add to this the idea of limiting your arm pressure to only the most demanding moments of your gig and your general playing ought to benefit tremendously.
In fact I'm surprised that I don't read this idea more often here. Simplest and easiest idea around! A true no brainer... Sure I've seen it written other places over the years. "Colin Lip Flexibilities" probably one of them although that ancient publication didn't illustrate the idea as much as i expanded upon it above. But it's there. Probably in Maggio too though he stresses the cruder versions of it ala 1 & 2 above in his "Maggio Monkey"
And to some extent I'm a hypocrite though less and less these days. I tend to forget to push my chops forward early on the gig or rehearsal. The likely reason is that over time I've been drawn to using the concept mostly as a last gasp life preserver in the sinking boat of four hour gig weakened endurance. But it needn't be limited to just the ninth inning.
Then again in some ways it doesn't matter a heck of a lot to me if I pucker early on a gig or not. I get exactly the same sound, range and volume regardless of playing with or without the forward lip push against the mouthpiece. And I've been doing it for 48 years next autumn.
But its still a good idea.
So why wait until the end of the night to pucker up?