Should I accept tenant with 1 cat if we advertise "No Pets"

[Vitaly Evdokimov]

Hello,

Should I accept tenant with 1 cat if we advertise "No Pets". We have have new tenants in other units without pets. 

The tenant is great candidate except that she is willing to stay 6 month instead of 12 month. So I was about to wave security deposit and last month rent because she is signing 6 month lease. 

Whats your recommendation? Should I say "sorry no pets" or wave "no pets" policy.

Please advice as Im not sure if that might bring questions from other tenants. Or other perspective tenants might go back to me and ask why we declined them with a pet and accepted this woman with a cat.