Landlord: Replacing dead pet violates lease

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Question: Is it legally binding to state in a lease that an existing pet is agreed to but that no more are permitted and when the said pet dies it can't be replaced? I am buying a duplex and one tenant has two cats and a bird. I have seen what damage cats can do when they decide to stop using the litter box. I want this building to be a "no-pets" property. I would not be so cruel as to tell her to get rid of her cats, and as for now, the apartment is clean and smell-free. I had this agreement in a lease on a property some years back. The tenant claimed "amnesia" and replaced her dead cat with a new kitten anyway. I just wonder if this arrangement can be binding and cause for eviction if not abided by. This tenant really wants to stay and we'd like to keep her, but I don't want any more animals. Landlord attorney James McKinley replies: A "no-pets" policy is certainly enforceable with a few exceptions. For instance, a landlord may not refuse to permit an individual that i...