I have a problem with squirrels, but no pigeons.
I have a bird feeder in my yard and feed cardinals in the winter. Cute birds (I'm not talking about the sig pics of other members, but the cardinals lol...though Mr Lucky's shower scene pic also contains cute birds of a different feather). I have modified the feeder to be squirrel proof and raccoon proof - fortifications, etc. They squirrels cannot eat at the cardinal feeder, much as they try. However, the cardinals while eating drop some seeds they are less fond off and they fall to the ground. The squirrels then have learned to sit under the feeder and eat the leftovers the cardinals drop. The result is a bunch of fat squirrels that breed and now I have about 10 squirrels who frequent my backyard. I have sonic anti-rodent devices in my house that means they do not try to get into my attic - they are content (now) to live in the backyard trees and build nests. No real way to get rid of them without poison, but neighbors dogs and cats stroll through my backyard, as to rabbits and ground-feeding birds, so I cannot use poison as I don't want to take out the neighbor's pet. The big traps are a pain in the ass and where does one release the creature anyway? Spring loaded rat traps might work, but again, collateral damage could result with cats setting them off and breaking legs, besides I'm not out to kill the Easter bunnies lol. Shooting them with pellet guns is inhumane as it isn't enough to kill them and would just wound. Tabasco type pepper laced food isn't great as again other animals could eat it and go nuts/suffer (like me when I drunkenly ate a wasabi roll once on a dare lol). Even if I did manage to evict the critters, with a food source there, more would just replace them, so I guess I will have to continue the truce DMZ with my not going after them if they stay the heck off my roof and out of my attic...after animal control removed them 3 years ago we sort of assess each other across the DMZ haha.
P.S. I tried the neigbour's dog - he runs into the yard to chase them but they just go up trees until he leaves. The best was when a red fox came strolling through...they went up the trees and he went right up after them and ate one for lunch - carried it away in his mouth. I thought he might decide my backyard was a great place to live with plenty of food, but he only came back once more then moved on and I haven't seen him since. The cats in the neighborhood are too fat to be bothered chasing squirrels.