CLOSED: Downy or Hairy Woodpecker?

We have a pair of small woodpeckers nesting in a tree in the backyard. I've narrowed it down to either Downy or Hairy Woodpecker but just can't decide for sure. I'm not good at identifying by looking at pictures. I hope someone can help with a correct ID.

My camera skills are awful so I will post a couple of different pic's to see if it helps. So far I only have pic's of the female. There are babies in the nest cavity and she's been going back and forth from the suet feeder to the nest feeding them.

A view of her back

She has a mouthfull of suet here

One more

I keep looking at my bird book and getting confused. It says the Downy has a shorter beak than the Hairy and this bird seems to have a longer beak than what I see of in Downy's. Hope someone can help ID from my not so clear photo's.

Thanks!

Downy - it's got black spots on the side of the tail (all-white in Hairy)

Resin

Downys have Dots,
Hairys Haven't

(phew!..that's hard to type-gave me a headache)

^_^

I already have a headache so I'm not going to even try to repeat that! LOL.


My Bird book says the outer tail feathers are usually pure white on both the Downy and Hairy but that the Downy shows black dots on its outer tail feathers. I didn't see any outer white tail feathers on either of the parent birds. The book also says the Hairy Woodpecker is not as common, so I was leaning towards the Downy. I just have a heck of a time trying to ID plants and birds from photo's and sure appreciate all the help I get here!

One thing I've noticed with these birds ... the female is more tolerant of me being nearby while the male will chatter and fly about trying to get me to go away! I've been trying to keep my distance as I don't want to distress them too much.