Just saw a big, fat tree rat sitting on the fence by my garbage can (a.k.a. squirrel diner), retrieved the 10/22 and my box of powderless .22 shorts.  Slowly opened the screen door, and low and behold there is the first squirrel's little brother about 10  yards away on the ground.  So, load the first round, crosshairs on the head of the little guy, a little whisp of muzzle blast, and that satisfying "thud" of a good hit.  Squirrel does the funky dance and flips around, going behind the shed.

I creep out in the yard a little more, and ole' fatty is still on the fence.  Take aim as he turns sideways to check me out.  Crosshairs right behind his front leg, and again a nice "thud" as the bullet hits.  He goes flying off the fence, and I run back in the house to put away the rifle.  Go back out, look around, NOTHING.  No blood, NOTHING.  Walk over into the neighbor's yard, and some little bastard is letting me have it from way up in the tree.  I don't think I've ever heard such commotion from a squirrel before.  Guess I just pissed him off.

Where is the best place to hit squirrels with these low-power .22s?  I have had good luck before with body shots, but today, nothing.  Any ideas?

(BTW, I have to use these rounds, I live in the middle of town)  

You may well have punctured their hides.  They may now go off and die.  BTW, I prefer to call them Bushy-tailed tree rats.

All I can say is where do you buy powderless .22 shorts?  I didn't think that a 10/22 would feed short ammo...

These are "Aguila" or something like that.  It won't feed them, it's a one shot at a time deal.

Quoted: All I can say is where do you buy powderless .22 shorts?  I didn't think that a 10/22 would feed short ammo...

the powderless 22 shells are called either CBs made by CCI, or colibris made by aguila.

i think there is a 10/22 conversion that will allow you to use shorts

here is a link to the conversion, kind of pricey though

www.rimfiresports.com/merchant.mv?Screen=PROD&Store_Code=RSC&Product_Code=VC10SK&Category_Code=R1A

Update:

Third shot just fired.  Sucker flipped around like crazy, then ran off.

I haven't tried the Aguilas but everybody I know who has loved them for urban squirrel use. I have a 8 month old Mountain Cur I am training and needed a squirrel the other day. I saw a good one in a tree at the edge of my yard. I got the Marlin 39A out (I love that gun) put the front sight on right between his front legs and centered it in the rear peep. Touched it off and bushytail fell straight down.
 Went out there about an hour later and the squirrel was gone. This is with CCI CB caps. There are a lot of cats prowling here so I chalked it up to them. The other day I got a shot at one and popped him in the neck. He went right down for keeps. Same round.

I don't know what the problem is, seems like when I shoot them in the wintertime, they usually are guaranteed to be DRT.  Some kind of winter fur factor?  Who knows.

Used to use CCI CB Cap in my Beretta 21A to hunt for Bufo frogs in my back yard at night.
Used to bait'em with dog food and then go out with my pistol and flashlight.  The bullet would penetrate those frog top to bottom.  Got as many as 5 frog in one night.