I've taken to a loose hold and have improved my scores on my range. I also just shot my first ten rounds of "premium" pellets. This seems to have made the biggest difference.
I'm shooting a distance of 15 yards at a 5 1/2" gamo target (and pellet catch). It has rings scoring from 10 to 1, so my maximum score could be 100. Shooting from standing position, offhand, I was averaging about 62 (55-70 maybe)... with the premium pellets I scored 75 on my first round. Looking forward to shooting these some more. The appearance of the pellets seems more refined over the standard. They also seem to fit the barrel more consistently.
I tent to stay with heavier pellets because IMO they are much more accurate. Even with cheap lead pellets I can still nail a squirrel at 35 yards from my office window.