I shipped a fragile disney traditions item around the start of the year, I purchased some construct-bots at the same time to pad out the box so it wouldn't ratle around much.
I also marked the Disney statue as a gift, without wrapping. there was no extra cost.
I recieved the box and as well as being tightly packed there were air pocket bags added to stop stuff shifting around.
I don't know if it was due to the fact it was a statue and amazon was taking extra care, or if I marked it as a gift which caused them to take extra care.
marking something as a gift doesn't have an extra charge.
Thought that might help.