Your little hawk is likely a sharp-shinned hawk, Dan. Take a look here: http://www.allaboutbirds.org/guide/sharp-shinned_hawk/id
Another small hawk is the kestrel (sparrowhawk) but it's much less likely to be found around yard feeders. http://www.pbase.com/wes242/kestrels

We have often watched a sharp-shinned hawk in our yard at home, chasing chickadees who always escaped. They are beautiful birds.

maeve