dude what is it with you and terrible selout!!
i like your edit, but those broken black outlines just look awful.
Maybe you could've brought that a little more....subtle?
Coffee:
The thing is, what's usually done is either no outlines, or outlines that MATCH the colours of the sprite.
For example: On the brown hair you take a darker brown, and outline it with that. And at places where the hair becomes lighter, you can also use lighter outlines.
Here, take a look at the outlines of my tree:

It's kind of the idea to 'adapt' the outlines to the sprite.
(In case you didn't know; the forum has a built in zoom function. Just click on an image to zoom in on it.)
Edit:
Here's an edit on coffee's edit:

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I changed the outline, but also made the skin tones more vibrant.