What Is It and How Do I Make It Go Away?

Can anyone identify this icky infestation? (Sorry the photo isn't clearer.) I don't even know the name of the shrub. I'm more into edibles, so this is a new one for me.

I tried picking the soft, squishy white with tan "heads/fronts" mystery creatures off by hand last year, but nearly every branch is affected this spring. There are also tiny ones on the backs of the leaves. That must be where they lay the eggs. The leaves curl up making it difficult to see them. Some of the stems have a black, mildew-like substance on them - I assume due to the presence of the mystery creatures.

I don't want to use chemicals. If this is likely to be an ongoing issue, I'd just as soon replace the shrub with something less vulnerable to infestations. Thankfully, I only have one of these, and it is relatively small.

Update - I don't know the exact name, but this is some variety of insect in the scale family. Insecticidal soap or oil are the recommended organic treatments I found. I'm launching an all-out assault this weekend.