Are there animals that would be detrimental to compost/bury in a garden?

Fish has a tradition of being excellent compost material, and I've seen others compost/bury various types of roadkill, chickens, and so forth with excellent results.

I was giving this some further thought, and I was wondering: are there any animals that would have a negative effect or be very inconvenient to compost?

One example that came to mind was turtles, and while I've never tried composting a turtle (and I hope I would never have to), I would imagine that the shell would take a long time to break down and also provide a barrier that roots could not penetrate through.

Some categories that might spark discussion/ideas, even if some of these might not have anything that fits them:
1. Animals that are too tough to reasonably compost. (turtles?)
2. Animals that have a tendency to bloat up with gas when composting and may unbury themselves as a result. (?)
3. Animals that carry some type of bacteria that can out-compete the soil life and cause issues. (?)
4. Animals with a large amount of fat. (whales?)
5. Animals that accumulate chemicals or other harmful to soil life materials in their environments. (?)