This morning I found a very sick rabbit (myxomatosis), which had decided to end its days in the hay that I was going to feed to some sheep. The thing to do would have been killing it swiftly; but I couldn't get myself to try and wring it's neck, being afraid I would bungle it and the rabbit would be in lots of pain! (Yes, I know I'm a sentimental softie and it's only a sick rabbit!)
I could, of course, have got the needle out and given it a lethal injection like we do for farm animals. However, I doubt I would have found the vene on that little beastie; plus - how do I explain the disappearance of a dose of barbiturate from the books? YOU WHAT???

So how do I go about it? What is the quickest and least distressing way of killing an animal like that?
By the way, I moved the rabbit into a different, sheltered position, so I could get at the hay, and it can at least (hopefully) end its life in relative peace.