What I do when I'm bird watching, Chico 2, is estimate its size compared to another bird, like you have with the crow, then look at my bird books. For instance, a Peregrine Falcon is about the same size or smaller
than an Australian Raven(aka crow), but then how big is your crow? You can often cancel out a bird as a possibility that way. You are very lucky if it is a Peregrine, I'm told they nest over in the forest opposite us but I've never been lucky enough to see one.