We dont have owls, kestrels or hedhogs were i live………The problem with the poisons is that they kill hedgehogs and other predators such as Owls and Kestrels.
A simple live trap will do it I got 4 in the last month, but you need to wear gloves so as not to leave any scent and not disturb the trap.
Best of all, but expensive is the gas fired squirrel traps that act like a humane killer. They can be set up to kill rats as well. A cafe had a lot of problems with rodents eating their way into food and waste bins and destroying expensive lids. He got 7 on the first day.
They have a counter on them which was good as the local foxes caught up quick and carried off the first 6 before he saw a dead one.