For those who think you can't control a Thompson in full-auto, here's a 16 round burst. (I counted 16 cases in the air, might have missed a few). And my subgun is one of those early WWII variants that is out of milspec -- it fires at 900 rpm instead of the expected 600, but the military had to waive compliance because it needed the guns. Note that the cumulative recoil pushes me back a foot or two, but the muzzle stays level.
Jim Land of NRA taught me the key. If you grip the Thompson as if it were a rifle, both hands firmly holding on, it'll start climbing quickly. (In giving the following instructions, I've got to reverse how I actually hold, since I'm cross dominant and shoot from the left shoulder. The following assumes the right shoulder is used).
Right hand grips pistol grip firmly, bears down. Left hand on forestock does NOT grip. It forms a sort of trough in which the forestock rests. At most thumb and index finger grip, and none too strongly.
Now ... think of the left hand, the trough, as doing the aiming. You keep that hand pointed where you want the gun to go, with minimal connection to the gun itself. The gun may rise, but the left hand stays where it is.
With each shot the gun rises slightly, then drops back into the left hand in time for the next shot. If the left hand were to grip the forestock, it would be pulled upward with the gun, then stay there when the next shot went off and pulled it still farther up, and the gun would rapidly climb.