Joe's "squeeze" is all wrist, LOL. It's a specialty cast used to get a tight loop with a short casting stroke, handy for casting in and around brush or obstacles. Also a squeeze when the rod is vertical can be used in a "tuck cast" to sink your nymphs quickly. Stopping the rod at a higher than normal angle with an overpowered forward cast works okay too, not as extreme as using the squeeze, which drives the nymphs into the water and creates a lot of slack to begin the drift.
He is an articed I just Googled that explains Joe's "sqeeze" in detail:
"My favorite cast with these type of rods is what I call a "Squeeze Cast". (see Joe Humphries superb video on Casting in Tight Brush)maybe the best coverage there is on the subject. The cast is initiated with the rod tip only inches from the water. The rod tip stops either at the 1:00 position or just a little behind you on a side arm cast. The casting hand is gradually opened during the back cast, the rod tip only travels a few feet on the forward cast and the rod is controlled with the fore finger and thumb thru the first 80% of the forecast. At the end of the very short fore cast, the three lower finger quickly close on the grip with a squeeze ! The thumb is pushed slightly downward against the top of the grip. The rod is then held absolutely at a "STOPPED" position with no forward drift of the casting hand. Hold position until 90% of the cast lays out and you are ready to drop the rod tip down (from the elbow) to present the fly. This short fast "SQUEEZE" at the very end of the fore cast develops very high line speeds and results in nice tight loops with no wind knots. Also be sure to keep the rod tip moving on the same level plane during both fore and back casts."
Link to the article quoted:
http://www.lasr.net/recreationarticles.php?ID=647