I can't remember where I read this tip but it has proved to be so helpful to me.
Before cutting out your decoupage it helps to put a bit of sellotape on the back of any intricate bits ... ie tails, branches and all tiny bits that you are liable to snip off.
I find it just gives that bit of extra support as there is nothing worse than spending ages cutting your decoupage only to find you've lost a tail or an ear ect.
Christina says ...
Decoupage can be so frustrating if you lose that tiny bit. You need lots of patience to cut them all out in the first place so to lose one .... well!!
Try Alexandrias tip and make it work for you and save yourself the time of searching for that elusive tiny piece.