Small birds (caged) and Fish... count as pets?

[Shawn Stiteler]

I recently just signed a lease on my first rental property. This property was listed as no pets. We did find a very good qualified individual to rent to. However at the date of the lease signing he asked if fish or caged birds were ok. I told him I would have to get back to him. Having never owned fish tanks or birds of any kind, I really don't if its even a thing to worry about possible damage or lasting smells. 

So the question is, Do you allow fish or birds in houses with no pet policy? If so, Is there anything to be concerned about or that I should be aware of as possible future issues? 

Would love to know your thoughts BP community! Thanks!