I know I've talked about this before at some point.
As we move our slides quickly (but not too quickly!), we need to keep that air stream very smooth.
It is so easy for the blowing to reflect the slide movement.
Trying playing a passage with silent blowing. Listen to your air stream as you move the slide.
I talk about this in the BoneTips portion of my website.
Here's a simple exercise that should help...