Sensitive Topic

There is no shame in controlling feral varmints of any kind wreaking the kinds of havoc on desirable populations the ways feral cats do; nor should there be any hesitation beyond employing humane methods to do so. Brain them with 30 foot-pounds of .22 and you'll not only minimize any (misguided) feelings of remorse and be doing your area a favor, but in many cases, also be doing the murderer a favor.
 
Things have changed from 40 years ago when feral cats or wild dogs were regularly taken out with .22 lr up to deer rifles and we talked openly about it. Wild dogs were very common in my neck of the PA woods and we’re devastating on chicken and duck farms. They were usually male and impregnated any female dog in heat they could smell. The locals didn’t tolerate the cat lady down the road either and so any cat that strayed on their property was terminated as there was few places that would take strays in. Today there are so many adoption houses that take cats and dogs and every other pet animals if you can catch them. I keep finding stray kittens on my property either dropped off or born to stray females. A call to any veterinarian will get you a local adoption person willing to take them in. Some require a fee to drop them off to cover shots or spaying fees. I’m still in the mindset that it’s cheaper with a well placed head shot and shovel on a cat I don’t recognize and no collar.
 
To the OP. 30lbs is plenty of power.. Place the pellet in the brain, not between the eyes! Not between the ear and the eye! Shoot it the brain... If he is facing you aim 1/4' below the top of his skull.. He will drop.. He still may twitch some. My old buddy said they are born with an internal coil spring.. HAHA .if he is to the side 1/4"-3/8" below top of head. Trust me on this. I've killed the shi! out of them... (state champ for two years) I'm Kidding only placed 2nd..

Our county and state laws are very good when it comes to animal control.. All pets owners must keep their pets on their property. Any cat or dog that comes onto my property can be shot / dispatched.. End of discussion... I don't have any issues where I live now, but years ago I had two neighbors ( white trash) that let their pets ( cats ) run loose and they pooped in my flower beds and urinated on my vehicle.. I didn't bother asking them to keep their pets up. I just used my FX Tarantula and killed em.. 5 gallon bucket, trunk of car/ went for a ride and buzzards ate well along side of highway...I did bait them to keep them busy as to place a shot..

Good luck with your critters!
 
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Let me first say. I am a cat person. I have a (one) feral that has lived around my property for many years. I like him. With that said. I’m a big believer in quick and humane death of any animal. So shot placement is critical. Looking at the skull of a cat and then at a stock photo. The eye sockets are huge. Bigger than you’d think. Taking up a lot of the skull. Looks like best shot placement is low in the ear. 
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Just be sure to be fully aware of what neighbors have cats and know whose cat is whose. Our big concern is taking out the wrong animal. 

 
In disclosing this problem, I hope that none of you assumed I would ever consider harming any of my neighbor's pet's. Nor do I advocate breaking any fire arms ordinances in and around my neighborhood. As of yet, I have not intentionally harmed one animal. In fact, I don't think I have the disposition to shoot a cat of any kind as I am a lifelong pet owner. I lived my formative years in a rural setting where I could shoot my bb gun and/or shot gun any time I wanted. Only once have I ever put a cat down(it was already very sick and on death's doorstep), and even though it was a clean kill with a shotgun, I can still see it in my head despite the fact that it took place a good 50 years ago. I've witnessed the the death and butchering of every kind of farm animal. I regrettably killed way too many birds and lizards as a child. I know exactly what a fresh kill looks like and even though I can understand that it is not feeling agony, it's death jerks are a kick to my heart. It would have to be a very extreme case in order for me to resort to using any weapon on a domestic animal. That being said, I was very close to having to euthanize a cat that frequented my property. He was obviously very wild and could not be approached- he was emaciated, his eyes and mouth were crusted over with filth, his fur was dirty and ungroomed, and he appeared to be in constant pain. It hurt just to look at him. Fortunately I was able to get him into a trap and to a vet's surgery. It turns out that that old tomcat was in the final stages of feline HIV. So they were able to kindly and painlessly send that animal to the other side for a nominal fee. This situation is what prompted my O.P.
 
The OP makes several good points in his latest post, almost all of which I agree with. That being the case, I have little doubt he will have the same change of heart about executing feral cats if (when) he experiences what changed my mind/heart about it. 

I didn't even start killing them after the SECOND expensive vet bill to reassemble our cats. Stupid me, even then I gave another feral cat another pass. BIG MISTAKE! 

Although that THIRD assault on our cats didn't require a trip to the vet, I killed the feral a**hole responsible for the carnage next time he showed his face! 

And every other one caught trespassing since then. That amounts to about 3/4 dead feral cat per year.

I wish I wasn't forced me to kill cats due to human ignorance. But 12 years into it I've learned to not feel any silly remorse about mopping up problems created by others.