Shooting free recoil

When shooting spring gun you would use a similar method. To maintain accuracy you need to allow the rifle to recoil and vibrate how it wants too. When shooting from a bench i do rest the forearm on my hand, not sure about others. And as for pcps.... anyone else know?

Most of the airgun benchrest shooters I have shot with use a method like what you are describing.
The way I have shot BR is to have only my trigger hand and my cheek touching the rifle. The grip of my trigger hand is very light, and when I fire, only my finger moves....my hand does not tense up. I have my trigger set-up very light so that I do not move the rifle while pulling the trigger. The cheek meld is so that I can have consistent head placement behind the scope. 
My other hand is on my rear bag for aim and stability.
I have found that when the rifle is shouldered, I get a small amount of motion from my heartbeat, which unless you can time it properly, can really mess up your shot.
Never shot PB's in competition, but that manner in which we both shot benchrest sounds the same.
Mike

Also when shooting a springer standing you use the artillery hold, a similar concept. Everyone has there own way but when I shoot standing the butt is not touching my shoulder and i pinch the trigger to keep my hand off the stock. I support the rifle only with one hand under the forearm. And I dont grip it, i just balance the rifle. But again everyone is different and ive been known to be wierd occasionally so some may think the way i do it is wrong. But it works for me.

Bench shooting is not high on my airgun priority list, but when I do, I shoot in a manner very close to what Mike Manabe is describing. Used to shoot BR with both rim and centerfires and shot both with as little contact as possible. Also why I prefer a single stage trigger that breaks around 7oz.

Absolutely jimreed1948, Honestly when I first got in to airgunning i didnt know pcps exsisted. I was surprised to find a whole community i never knew exsisted as well. Dont get me wrong I love my springer, but i wish someone had been there to steer me right haha.. And personally I wouldnt call the recoil an issue, more of a challenge to me but i agree pcps translate better to PBs.

I have tried shooting recoil free. It works good. I have shot several 1.5 in groups at 150 yds with my daystate air ranger. 25.

My set up is daystate air ranger .25 hawke sidewinder 30, jsb kings ,front and rear leather bags. The only thing I touch the gun with is the tip of my trigger finger on the trigger.It works well but I normally use a atlas bipod & rear bag with a good cheek weld.
The groups are not as good,but I never want to get to far away from my fundamentals.