Not sure yet, I've only been for small game once and didn't see any with the wind howling at 20 mph! I don't have a scope on my .22 either.

Don't
 

I never shoot off hand unless I have too. Every time your heart beats the sights move.

I shoot a .22 reset target almost everyday at 50 yards. which is a 2 inch bull. so ya I think I'd be fine on tree rats. Keep practicing you'll get the hang of it.
-Jake

I have hit a couple at that range with my 597. It is entirely possible-better odds with a good rest obviously. I love my 597-I put a 4x32 on it a while back and it's my go to gun for small game. Great shooter.

i got my .22 sighted in at 50 yards and hit squirrel at 25 yards. i shoot them from 25 to 75 yards.

"Does Charlie Daniels play a mean fiddle?" haha

We have a lot of fine off-hand shooters on this thread! Amazing and unbelievable.

i can put an entire clip of 22s in a squirrel silhouette, off hand, at 60 yards. if 40 is tough, rest off your knee, or use a tree, or even a mono-pod. the farther the shot, the more fun in my book