I had a rabbit problem in the garden. Everything I planted was eaten - we are next to a large field, so I bought an air rifle. I managed to shoot 2 or 3, but hit one in the foot and it screamed and screamed as it ran (hopped) away. Horrible!
I then set a few snares and once I got the diameter right, I caught lots and lots. 1 or 2 every day for the whole summer. I'm fairly sure they died quickly. You could tell by the way they were lying and the fact that the surrounding area wasnt disturbed. Myxomatosis killed them off 5 or 6 years ago and although the numbers have increased again, not many venture into my garden. Not sure why, but maybe It's me and my snares selectively breeding unadventurous rabbits.
Anyway. Snares are the way imho