When Bill Toney (?) was an instructor with Border Patrol, there was a demonstration at the range in El Paso--
He fired both from high hip (underarm) position and from the shoulder and did some real magic with short bursts--two to four rounds. He rested the fore grip, either vertical or horizontal, or the magazine, on the open palm, and allowed the Cutts Compensator hold the gun down. He showed that a full 20-round mag can be kept on a silhouette target at 50 feet, using this technique.
Later, in a magazine article, Toney was quoted as saying that most people take a death grip on the fore end, and the recoil lifts the muzzle anyway. This tight hold just keeps the muzzle at the higher position, and subsequent rounds lead to some pretty spectacular muzzle climb. Resting fore end or magazine on the open palm allows the gasses directed upward from the comp to drop the gun back onto the open hand.
This technique is depicted in the old movie, "The FBI Story," starring James Stewart. The agents are shown on the range shooting vertical-foregripped 1928 guns with the 30-round magazines in just this manner.
Of course, it is not necessary to have the hand opened flat, but you should NOT grab ahold and try to keep the muzzle down by brute force. A partly closed hand is okay, but, as noted above, the shooter should RELAX the forward hand.
I have taught this technique to people who have never fired a submachine gun. In under 50 rounds, they can keep short bursts on target at 20 to 30 feet.
The same procedure works, though not as well, with non-compensated Thompsons. I have yet to find ANYTHING that works for accurate full auto fire with an M2 carbine. There, you use semi for hits, full auto for sound effects.
Best,
Johnny