Make sure your insurance doesn't have any limitations on animal breeds or, if it does, communicate them to your tenants. 

My pet addendum states that only the listed pets are allowed (by name and breed).

My wife is a damn proud white AFRICAN American, a REAL African American, born breed and raised in Africa, immigrated to America via working for next to nothing for years on end to eventually earning citizenship, yet judged and assumed who and what she is because of skin color..... 

Roaches are absolutely disgusting and will breed and take over a home  (they likely already have), and mice--- mice will chew on wires, electricians are expensive!   

Do you have a pet policy, does it ban aggressive breeds?

However you must be selective in choosing dogs, you must not allow any dangerous breeds.

Some people, on the other hand, have studied dogs for many years and have wonderful "agressive" breed dogs.

You can discriminate however you choose against breeds, sizes, etc.

-require that any renter that owns a dog (of any breed) provides documentation that they have been to some form of obediance class.

I have always been a animal person but I have had to implement a no dog policy cause my insurance won't allow so many different breeds so have found just easier to not allow them.