What sci-fi book is this?

I had a paperback book some years ago, one of those “best of science fiction/fantasy” things, full of short stories by various authors. Some stories I think were excerpts from novels. “Invasion of the Body Snatchers” was one of them. The story I’m interested in concerned a future in which there are slave-humans whose ancestors were animals. Their genes were tinkered with and though the creatures look human, they are not treated by the law as human, but are considered servants to “real” humans. For instance, a turtle human can live a very long time and is put to work as a guard in some underground enclave. An animal-girl is put to work as an “escort” and a “real” human girl snarls at her with jealous rage because “she’s not a person, she’s just an animal that looks like one.” The story is about a rebellion brewing among the slave-humans and their quest for legal rights. Is this a novel or short story? What is the name and author? I’d like to read it again sometime, it’s one of those odd stories I’ve never been able to forget. It’s NOT The Island of Dr. Moreau.)

It doesn’t sound exactly the same, but parts of this sound like the Future History imagined by Cordwainer Smith, in particular his story The Ballad of Lost C’Mell. It’s anthologized n The Science Fiction Hall of Fame Vol. 1, and in The Best of Cordwainer Smith (out of print, sadly, but obtainable thrugh used-book sources).

THAT’S IT!!! Thank you so much, Calmeacham! You have made my day!

Here’s a list of anthologies that contain this story:

http://www.sfsite.com/isfdb-bin/pwork.cgi?a0143