I just got back from the range today (first time I've shot since August). I was shooting quite alright though. I rented a USP .40 since I'm too lazy this week to clean my own guns.

I put a target out at 15 yards, and I could put a good grouping (4" in diameter) BENEATH the black 9-10-x ring. This was done to a NRA 25 yard rapid fire target. It seemed like this was the natural point of aim for me, given the height of where I was standing and the target's height.

Is there anything I can do to put all the rounds on a bullseye, or is this expectation normal? It seemed that when I wanted to change my point of aim, I got sloppy (think, I have a natural arm extension, and if I try to elevate it beyond the horizontal, I lose my balance...going lower is not a problem). Should I change my weight balance, flex my knees, or what?

This is why i need a .22 pistol. I need to teach myself good technique so I can hit what I want, and when.

themao
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Got ice picks?

Or then again, it may just be where that gun is sighted in and not you at all.
Of course on your own guns, you would regulate the sights to point of aim.
On that rental piece, you would have had to hold it a 12 O'clock to get the bulls-eyes.

I'm guessing its the gun and ammo combo and not you.  Try another gun with adjustable sights.  Adjust the sights all the way up, shoot a group.  Adjust the sights all the way down, shoot a group.  You should see two different POIs.

shoot shorter suckers

Quoted: shoot shorter suckers

Fidgets?

You may be fliching.  When I have that problem, I get out the shotgun and put a few slugs through it by firing withou putting the buttstock in my shoulder.  In other words, I hold the gun in front of me.  Then the pistol doesn't seem to recoil nearly as much, and my flinching goes away.
You might also have someone put a snap cap randomly in the magazine and see if you pull the gun downward upon pulling the trigger when the snap cap is loaded.  Many times your hand will pull the pistol downward in anticipation of recoil.

sounds like you were using a 6 o'clock hold, a lot of european makes are sighted for the front dot to cover the target.

Then again, maybe I am nuts and I just shoot like crap