Woodpecker with Black Dots

The weather is very foggy so I should have headed to a harbor to catch a shot of a hazy boat.  But I had it in my mind to find a bird, so here he is.  Due to his size I thought it was a Hairy Woodpecker, but I think I was mistaken.  My Cape Cod bird book says that Downies have black spots on their white outer tail feathers.  So a Downy it is.