What about not wrapping it at all? Every year Santa leaves one or two presents under the tree for each kid that is not wrapped. When they come out, they get to be excited about it, play with it, etc, with no help from Mom or Dad to unpackage, watch unwrap, etc. We are there, and usually video taping, but it just starts the day off in a fun way and make it easier to get coffee, get going, etc.
With little kids, I find it best to have everything out of the package upon gift giving time, if possible. No kid wants to just pile up a bunch of fort knox-like packages and not play with anything just a little between presents.
We usually have santa leave each kids big present out unwrapped.