How "natural" is a wire fence? That's about the only sure rabbit
preventive.

But,,, make sure the openings in the mesh part are very small. I thought I had
my rabbit problem solved until I noticed a large amount of dill stalks laying
on the ground, and many of my green beans chewed on. It was 2 baby rabbits,
just small enough to fit through the holes. It didn't take very long, though,
for them to grow too large to fit through the fence, on a feast of dill and
green beans.
Sue in Mi. (zone 5)