Dale,
Some times we even surprise ourselves, eh.
My grandfather was never an avid shooter, but even he would marvel at the head shot squirrels that I brought home on occasion. 
My Remington 513P came with excellent peep sights, but it was still difficult to get a squirrel to sit still long enough for a head shot.
Speaking of rabbit hunting, years later while stationed in Denver with the AF, we visited friends in Casper WY. Never saw so many rabbits in one place, in my life!
We were only there overnight, so two of the friends husbands loaned me a spare rifle, and took me rabbit hunting. We hunted just the afternoon we arrived, and again for a few hours the next morning before we left, and came home with thirty-two cotton tails in the trunk!
We got caught in a near blizzard on the way home, and arrived very late. I had to call a friend to help me finish cleaning them (field gutted only during the hunt), and split the meat with him for his trouble. We ate delicious fried rabbit for months!
Passed through Casper again a couple years ago, and there is nothing but sub-divisions where we hunted.
dB