I have been shooting cotton tail rabbits with a sub 500 fps GAMO at 15-20 yards- head shots flip them right over.
now-the next story you can believe or not-but I can verify it first hand.The nursery I am shooting rabbits on is fenced but somehow a doe got in there and was causing the owner considerable damage to his newly grafted fruit tree stock,and they asked me to bring over my crossbow and shoot it for them.I declined as they did not have a permit-but I said I would come over and see if I could help chase it out the open gate.
As I walked around [after dark with a light]-I spotted a dead deer under the kiwi trellis ,starting to bloat but no smell-so I figured it had been dead under 24 hours. It had one small puncture wound high in its neck,which I figured had hit the jugular and it bled out internally.I went back and asked the owner if he had shot at a deer-he said he had the night before as he attempted to chase it out,he said it had been in the fruit trees, he shot it with his .177 air rifle,and it ran under the kiwi's-where I found it dead the next night.now-we knew there was only one deer on the property-he admitted shooting it with his air rifle,and I knew that was the only rifle he had[he is elderly,and had just bought the air rifle which I had sighted in for him,so he could shoot starlings in his cherry tree]so I concluded this deer had died from one single pellet that nicked its jugular[they were the pointed hunting type pellets] shot at close range-probably under 10 or 15 yards.
so-you can believe that or not-admittedly a freak shot but I found the deer -it doesn't prove much except even a sub 500 fps pellet can be lethal if hit in the right spot at close range -these aren't toys.