Here's a blog post about Eleonora's Falcon (Falco eleonorae) and a unique behavior for a predator.
The authors of the original paper report that this species caches live, but disabled, prey (small birds) in rocks, purportedly to keep the prey fresh. The falcons disable the prey by removing primaries (outermost 9-10 wing feathers) and retrices (tail feathers) and stashing them in rock crevices.
I think a commenter in the blog brings up a very good point. Injured prey are very likely to seek out crack and crevices and hide. My students will tell you that if you give a the smallest crack in your hand you'll lose the bird. Like mice, many birds are extremely adept at moving with their feet and I'm skeptical that birds could be held in the manner described.
I suspect that the falcons are exploiting the escape behavior of the birds. Still, and to entirely anthropomorphic, this stuff has got to be terrifying for a small bird.