Now wait about that hawk/pigeon thing. I've got a newspaper article about a hawk trying to eat a chihuahua. It was being walked by a little old lady on a leash and the hawk dove and the dog was airborne! The woman had a tug of war for couple of minutes. The dog died from injuries.
Also, I was walking in our neighborhood. La la la, walking, walking, "oh look at the fat little mourning dove in the yard right there, like 4 feet from me." BOOOOOM! Out of nowhere a hawk dove down and in milliseconds, no more dove. Not a sound was heard. I could only stand there, in shock. Not a trace of anything amiss, just what was burned into my brain.
So I think a hawk would go for a pigeon, no problem.