Let me say amen to no poison.
Our great dane found and ate rat poison in my mother in law's store room. Thankfully, I caught her chewing something unusual and found the green tablet and realized what she ate. Called the vet and he advised to give her hydrogen peroxide. She threw up several tablets. The vet gave her vitamin k shots and prescribed vitamin k tablets. She survived without incident; however the experience was stressful and expensive for her owners.
Undetected, the poison may kill your pet in a very gruesome way, bleeding to death in a visible manner.
Rat poison can cause big problems. and I would not recommend it.
Regarding traps, I have used the plastic clam shell looking traps (Lowe's has them) with good success, baited with peanut butter and dry dog food.
Peppermint sounds interesting, perhaps preceded by incense, if you are old enough.
Regards,