I tried that (digging around) and I don't think I dug enough. I was worried about tender root growth. We have to keep a hefty gate around our garden to keep the deer out, but how I wish we could have some "barn" or outdoor cats to protect us from the rodents. Sadly, there are far too many eagles along the coast here, and our neighbors haven't recovered from the loss of their sweet kitty who was plucked from the yard in plain view. They've actually found collars of missing pets in the eagle nests.
I do see the occasional crow nab a rat from time to time.
It's always us against "them".
The "them" are the critters that remind us that what is ours, is theirs too!