Don't buy things with a lot of wrapping. Or, if you are packing things, don't include a lot of wrapping.
Think about it, what happens to all that wrapping? Chances are in finds its way to the garbage can, which leaves you and it is not your problem right? Well, it then goes to the dump, or to be burned, or whatever it is that happens in your part of the world.
The dump is a big waste of land, that nobody will ever use later in its life. Burning sounds better right? But no, it is putting harmful, or not so harmful but bothersome, things into the air to bug people and the earth.
It is biodegradable you say? Wow - so much better!! Think about it, if it gets put in with the regular garbage, is it really any better off? Nobody is going to come around years from now and be happy that your few items aren't there, they are just going to see the pile of other things next to it that you, and others also tossed out.
So, the less packing, the better.