Re-reading some of Elmer Keith's works recently, I note that he recommended the "cup and saucer" approach whenever possible for game shots . . . that is, holding the gun in your primary hand, and resting that in the palm of your off hand, merely as support. He recommended not attempting to control recoil at all, just maintaining a secure grip to avoid dropping the gun.
Jeff Cooper, on the other hand (sorry), when developing his "modern technique", built on the Weaver grip in which the off hand wraps around and firmly grips the shooting hand, applying the "isometric tension" in an effort to control recoil to the extent of being able to get off quick follow-up shots, since Jeff was more oriented toward combat shooting.
The biggest mistake I see novices make in this regard is in applying a death grip that turns the knuckles white, almost assuring a pronounced tremble while aiming. Ya gotta hang onto it, but ya don't have to strangle the poor thing. Heavier-recoiling guns do require a somewhat more secure hold, but you pretty quickly discover just how much is necessary. No magic involved.