Growing up back east our cat was a tough old cat. One day he started showing up each morning with patches of fur missing and some signs of fighting. Our cat never came home looking like this before. If you are overly sensitive on animal abuse you may find my following solution to the problem rather unwelcome.
As much as I'm against animal cruelty what I did was something I do not regret. This was a wild feral cat who I'm sure was harming more than our cat. I'm still believe that what I did but it was a good thing.
Well, for me a BB gun solved the problem of a varmint in our back yard.
Generally speaking, squirrels are there because there is stuff there that squirrels eat.
If there's food, they'll hang around. Eliminate the food source and the squirrels will move on to greener pastures.
Instead of regular seed, try safflower seeds in your bird feeders.
Birds like 'em just fine, but squirrels don't like safflower seeds.
Aside from physically catching them and transplanting them, there isn't much else you can do.
There's always the "If you can't beat 'em, join 'em" train of thought, and that is to also set up a designated squirrel feeding area. They would much rather go where the chow is easier to get to than to try to break into squirrel proof birdfeeders full of safflower seed.
Watching them in a specified control area can be entertaining.
Maybe just a kind word to the neighbors along the lines of "did you know that colorful songbirds love xxx, and squirrels won't try to steal it?"
Maybe I'll just put up the owl.
I asked my friend Carl about your squirrel problem. He said you just have to make them some friends.
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I wondered how long it would take for a Caddyshack reference.
Personally, I'm a big fan of my Sheridan Blue Streak. It's quiet and works on everything from starlings to rabbits. Lay up in a blind (the kitchen or dining room window, open for obvious reasons and a couple feet back so the pellet gun isn't sticking out where neighbors can see it) and wait.