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I don’t know what kind of acerage you are hunting but if you haven’t tried a .17 hmr yet, your missing out. They are deadly accurate. You can literally just do head shots all day long. If you shoot for the vitals, sometimes you will almost cut them in half. Rabbits must have a softer hide because it almost looks like a crime scene if you shoot one of them. Savage sells for around 175 bucks so they aren’t to bad pricewise. Probably one of the funnest guns I own, they are that good.
Holst and I can attest to that. Once up at the Hukriede Compound on Mille Lacs we took turns turning chipmunks into a fine red mist with my .17. 
So last year I am in Pine City with my kids, and they have all 4 of my .22’s in use, so I used the .17. (You absolutely HAVE to head shoot only!
) Anyways, I see one of our elusive black tree rats. I have always wanted one for the wall. But I knew what this gun was capable of…so I knew I had to take a shot that would do the least amount of damage. Honestly, I put the crosshairs on the juglar vein….and squeezed. 30 yards away he dropped dead as my ex wife’s personality. 
That squirrel now resides on the wall in my basement waiting for a white cousin. 
A .22 non-hollowpoint round would be my choice. You can shoot from a distance yet, and maybe pick off more than one. 