I have come to the conclusion that having the head of the animal still attached is
good luck. See the following for an example:

In addition to this inference, below is a list of things the Chinese guides have told us that chinese culture regards as good luck:
NOTE: Magnolias, Crab Apples, Pine trees, rocks, and the color red represent benevolence, which is the only thing they look for in a leader other than the leader's ability to over through the previous ruler. Chinese culture says that if you can overthrow the ruler, you assention is intended by God. If you fail, God obviously did not favor your rule.
They haven't really ellaborated on what gives you bad luck, but they have told us the following tidbits, which seem to at least imply bad luck:
- If you put a dragon in your yard during the Qing dynasty, you and your family and neighbors get killed
- If you paint your roof yellow in the Ming or Qing Dynasty, you get killed
- In Gungzhou, they used to eat monkey brains and fetal rats until the practice was banned a few years ago
- Stealing pearls
Sort of like our culture, except totally different.