Droll Yankee has a wonderful bird feeder, that has a ring around the
bottom. When any bird too big (or squirrel) tries to get on the bird
feeder, it spins the ring and the squirrel or birds get flung into the
shrubs. I got it for squirrels (which is very entertaining actually).
But it also works for pidgeons and grackles (which we have an
infestation of.

Also, putting out different kind of birdseed helps. If you put out
corn, you'll get pidgeons, mice, squirrels, etc. If you put out a blend
that doesn't have corn (but has sunflowers and thistles, you'll get
cardinals, jays, swallows and the smaller birds). If the pidgeons go
for the seed on the ground, I just open the door and let the dogs out.