This hawk was puzzling me. It spent last week flying around the neighborhood and calling and calling--far too much to be hunting. Finally, I got a picture and asked on the NatureNet forums (I do like having a whole world full of people to ask questions of!)
Turns out it is most likely a sharp shinned hawk (I'd have guessed a peragrine, but then, I didn't even know there was such a thing as a sharp shinned hawk) that had recently left the nest and was begging its parents for food.
It seems to have widened its range now a bit, and to be calling less, so maybe it has figured out how to do its own hunting.
The nature-netter who answered my question also sent a nifty link to a page on sharp shinned hawks. Seems most of the birds I've thought were peregrines were probably either sharp shinned or Coopers, since peregrines are aerial hunters and thus unlikely to find swooping down from telephone poles a practical way to hunt.
One of these days, I hope to have some of the answers, myself, but since I decided to start looking at what was happening around me in nature, in the city, I've been inundated (bugs, birds, plants, more bugs...). So, for now, I'm very, very happy that there are people out there willing to answer questions and explain matters.
Edit: I inserted the link on Sharp Shinned hawks this time!