Often times its things that we already have, that can assist in tidying up your ornaments. You might have heard of egg cartons for craft purposes. Why not also use these for storing delicate tree items? Set aside some clean, durable egg cartons for this purpose.
Also, when it comes to wrapping paper and gifitng accesories, avoid holding on to anything that takes up space, which has lost its flare. Many papers can be prone to fading or tearing. Just start fresh as new wrapping can be very affordable. Or better yet, innovate paper from comics in the newspaper. A holiday themed comic strip would nicely stand out under the tree.
Speaking of the tree, do choose to save the pieces acquired after your tree has been trimmed. They can make easy mantle additions, and will smell far better than a plastic accesory acquired from Cost Plus etc. Enjoy them, and then discard them. One less thing to pack away afterwords.