@Catlynn I'll keep an eye out for that! Even my scrub jays, who normally make a dramatic entrance every time, hide silently in the scrubiest trees when the hawks are around. Nothing scares a bully like a bigger bully, I guess; and I've never seen the woodpeckers bullying the other birds.
(I named the scrub jays “Jack and Jill” after the “Puss In Boots” couple.)