My daughter shot her elk with her Handi resting on a a set of Caldwell 9"-13" bipods, and her deer off a set of Bi-Fur pods (cross sticks) I made.
In both cases I think the rest raised the POI several inches. Her gun shoots pretty decent off a concrete bench with a shot bag of sand under the hinge pin and another under the buttstock. I suspect muzzle jump in combination with an unsupported buttstock raises POI. I really need to do some controlled testing with both rests, unless someone here beats me to it.
