"I will not use a .308 on rabbits or squirrels"
I don't see why not. A 100 to 120 gr. cast bullet over something like 5.0 to maybe up to 10.0 gr. of Unique make a great small game load and lets you get more use out of your big game rifle.

I even run small game load from my .35 Whelen with a 200 gr. cast bullet over 10.0 gr. of Unique.
Paul B.