N/A Overkill on small game

In my simple mind, it's a matter of energy INTO the right part of the target makes the kill, every bit of energy that passes through the target (and/or passes through a non-vital area) is not needed. Getting a decent trajectory and a manageable time to target is the other side of the same coin. How fast do I need to shoot? Each gun and ammo combo has a best accuracy solution - it is really up to you to find that magic recipe.

That being said, my .25 is around 40-ish FPE and I have backed my .22 down from 45 FPE to ~22 FPE for air usage considerations. I still get almost 100% pass through on squirrels with the .22 Hades at 22 FPE, even over 50 yards. The lungs, heart and head do not offer much resistance to the pellet. A gut shot, while lethal, has much more fluid and squishy stuff to absorb the energy.

For Coon, I would edge over 50 FPE in either .22 or .25 - and be sure of your aim. Coons are very tough, and an injured coon is wildly unpredictable. Yes, they can tear you up. Don't be fooled by the guys on the 'net that have a good bait station and a solid shooting position, shooting Raccoon is not for the casual BB gun guy. 'Possums are not common around here, and it has been shown that they are beneficial to the environment. Not sure I would seek them out for removal unless they were a persistent annoyance.
 
I'm in agreement with JimNM. I get good results on squirrels with my 19 fpe 177, and 18 fpe 22 but they do drop a few steps faster with my 32 fpe 22 and 25. But anything much beyond 30 fpe (possibly upper 20s) in a 22 is overfill in my opinion for small game. But this is for inside 50 yard shots and if you need to take longer range shots (and have the accuracy to do that sensibly) you would need more fpe. All 10 shots I've take with a 32fpe 22 passed through and 16 of 18 with a 32 fpe 25 also sent through a squirrel and exited. The other two were front of chest shots that ended up under the skin behind a rear leg.

I killed a small raccoon with my 32 fpe 22 but it took three shots. I killed another small one with my near 50 fpe 25 and it was one shot and immediate death. These coons weighed less than 10 lbs and they can get up to around 50 lbs. Much bigger animal and not easy to kill like a rabbit. Even with 50 fpe I think they need a brain shot to get immediate death.
 
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I'm in agreement with JimNM. I get good results on squirrels with my 19 fpe 177, and 18 fpe 22 but they do drop a few steps faster with my 32 fpe 22 and 25. But anything much beyond 30 fpe (possibly upper 20s) in a 22 is overfill in my opinion for small game. But this is for inside 50 yard shots and if you need to take longer range shots (and have the accuracy to do that sensibly) you would need more fpe. All 10 shots I've take with a 32fpe 22 passed through and 16 of 18 with a 32 fpe 25 also sent through a squirrel and exited. The other two were front of chest shots that ended up under the skin behind a rear leg.

I killed a small raccoon with my 32 fpe 22 but it took three shots. I killed another small one with my near 50 fpe 25 and it was one shot and immediate death. These coons weighed less than 10 lbs and they can get up to around 50 lbs. Much bigger animal and not easy to kill like a rabbit. Even with 50 fpe I think they need a brain shot to get immediate death.
Only coons that are gonna get up to 50# are pet coons, in the wild a huge coon is 25#, I trapped and hunted them for a long time the biggest one I ever caught/killed was 24# and was over 40 in long nose to tail huge skinny body. Guy I used to sell furs to told me he had something to show me when I took some furs in. He went in the backroom and came out carry something in both arms it was a raccoon that weighed 58#. Some guy jumped a persons fence in town and killed their pet coon and brought it to him to try and sell it, of course he called DNR and they arrested the fellow who ended up in all kinds of trouble.
He was keeping coon for owners until they decided what they wee going to do with it.