I had one of those little bastards drumming my house too. I took an alt. approach. If you search on the web, you can find .wav/.mp3's from some tech device that plays sounds to scare birds. In case of the woodpecker, there are two of them. One is a sound of an injured one, the other is a coopers hawk - one of their predator birds.
Just burn a quick CD with injured/15 mins silence/predator/15 min silence, get a portable cd player and some computer speakers you don't care about, put it outside where they're being a problem, start it on loop, crank up volume (as it won't get too loud w/ unpowered speakers) and walk away for awhile. (make sure you are using an a/c adapter on cd player so batteries don't die off) I went this route, as every time I walked outside to catch them, they'd fly away too quickly to be able to get a shot off them.
They haven't returned since... Pigeons on the other hand, get your bbgun ready.
