Who could be visiting me (and how do I keep them away)?

Somebody has been digging up a few of my pea shoots every couple nights, and I would appreciate if they stopped! I've seen possums and stray cats in the backyard before, but it's fenced on most sides with 8ft wooden boards, except for a chain link fence abutting the house behind mine, so I doubt it's deer. I suppose it could be rabbits as well, but those I haven't seen around my neighborhood.

For ecoregion reference, I live in the Country Club West watershed, a little east of I-35 and a little north of US-71.