Regarding this small hawk's identification, you have two options. If the hapless victim is indeed a sparrow, that puts the hawk about as big as a pigeon and this is the sharp-shinned hawk. The prey looks to me to be a robin, what with its distinctive orange breast. In that case, the hawk is about as big as a crow, making it a Cooper's hawk. But the story's not over: you would need to account for the larger size of sharp-shinned females. So before I put my money down, I'd want to take a look at the back of the head or the wing patterns. In either case, these Accipiters often stalk bird feeders for unsuspecting prey, making for entertaining or disturbing backyard scenes for the family (depending on the child's Y chromosome status!)

If you wanted to fit in with most Americans, you would call this a sparrow hawk and be done with it. But if you did that, you would be wrong, since the sparrow hawk is an Old World species. A final option is the American Kestral, but it has white cheeks and a mustache and is even smaller than the bird shown.

Check out this page to get even more confused:

http://www.birds.cornell.edu/pfw/AboutBirdsandFeeding/accipiterIDtable.htm

I've not yet seen either of these in Seattle, so congrats on the find!