Yes, rats. Both kinds. Brown Norway rats and gray, smaller Polynesian rats.

When did it start?

We noticed rodent droppings in our ground-level attachment.
We noticed boxes that had been violated and film negatives were taken out and chewed.
We noticed small amounts of rat droppings in our attic.

When our son exclaimed a rat was in his closet, trying to eat its way into the attic, we checked - he was right. We caught it in a Havahart trap and released it in a forested area far from homes.
(We are true wimps, and do not believe in killing anything larger than mosquitoes.)

We are about to change our tactics. In spite of our catch and release on the other side of the mountains, and our 2-cat household, we still have too many rats. We are overwhelmed! We are driven to kill, big time.

We worry about poisons because if our cats or dog eat a poisoned rat.... we worry. Worry, worry worry. We worry about toxicity of rat poop, when we vacuum it up, etc., etc.,etc .

We responsibly compost all our vegetable waste. Guess who eats it? The Havahart traps are empty, cause our rats got smart, and ignore our delicious bait. (No, Mom! It's a monkey trap!) They have tunnels in our compost! We're FEEDING them!!!!!

Before I turn my house and home over to the eXterMiNaToRs.... I want to check in with those who have become my best and most knowledgeable friends... YOU!

CONCERNS:
Fumigation? Dead rats in inaccessible places rotting and smelling.
Poisons? Here, Fido, eat this rat, it's cool (evil cat).
Contamination: When we vacuum up the rat poop, will we die from the
poop decks... uh, poop dust?

Other options: Fire, nukes, midnight target practice with IR goggles, nitrogen tri-iodide.

I'm a bit of a pacifist, so I couldn't do glue traps. I drowned the first rat I caught in a live trap and still have flashbacks....

Are they edible? That might take some of the murder aspect out of it.
YUM! Ratkebobs! (BARF) sorry.....