Adverbly

I thought I'd talk about this, because I've been hearing about it quite a lot recently. But it was only recently that I'd heard about it at all.
Adverbs.
Adverbs tell you how something is done.
He walked SLOWLY.
I wrote SLEEPILY.
And then dozed off LAZILY.

You get the picture.

It seems like adverbs would be helpful. They give you an image, without taking up a ton of space in the process.
But a lot of serious writers avoid adverbs at all costs.
Why?
I'll write an example:

Scene 1: He spoke sleepily.

Scene 2: His words were slow, and slightly slurred as though they hadn't woken up yet.

Which of those sentences gives you a more vivid picture? Well, the second one. At least, I sure hope so.
So, adverbs work. But they can be very lazy, and not nearly as strong. "Very" is one example of a "very" weak adverb.
And in the wrong hands, some adverbs can just be awful.
If you take the time to set up a strong scene, you don't even need that adverb. You can immediately tell that someone is in pain, because of the way they're limping, gritting their teeth, and watering at the eyes.

So, did I go and delete all adverbs out of my stories? Well, no. That seems a bit extreme at this point. But I am trying to notice all of my adverbs, and to get rid of those that I can replace.