I had a few bird feeders out back, about 12 pigeons started to feed along with the song birds. They would all stay on the roof, which is not good. The droppings would eventually ruin the roof. I stopped feeding the birds altogether now. I still keep water out for them. I wish there was a seed that pigeons don't like. I guess I can put the suet back out. They won't eat that. Starlings I can live with. I will just feed the birds seed in the coldest months of the year when there is no other food for them. I get all kinds of birds out there. I nearly pissed my pants the other day when I saw these two yellow and black birds looking around for seed.
Become a falconer. Pigeons, squirrels, chipmunks, and rabbits all bailed from my area when i first started practicing falconry.
Falconer, I to wish to someday practice the sport of falconry, but to the OP I personally love pigeons, but as for the squirrels where I am at you can shoot them with your pellet gun
You can keep squirrels out of the bird feeder by putting a pie tin over the feeder. Hang the feeder from a string. Run string through middle of pie tin and place above feeder. Don't have any suggestions for pigeons though.