Eija, I also found that smaller leaves from all my birch trees were getting past the deer netting so two years ago I switched to shade cloth. Its mesh is fine enough to stop even the needles from our spruce trees! It's also UV protected for up to 5 years, I think. I weigh it down around the edges with rocks and support it in the middle with inflatable pool toys such as inner tubes and balls.
I get it mail order from Lee Valley.... don't know if they are in the States but shade cloth must be available at many other places.
Good Luck