How have you treated DUI in terms of accepting/denying a prospective tenant?

You will need to deny the applicant for some other reason;  credit and background check or other reason unrelated to the program.  

Some landlords deny for not having a verifiable rental history. 

I always prayed I could deny them.

Cash flow is tight in Phoenix right now, there's no denying that fact.

I denied applicants who didn't have personal checking accounts.  

If the breed of the animal means you can lose your insurance, then you can deny the animal - or rather their request for a reasonable accommodation - based on the request creating a financial hardship for you.But, since you've already allowed it, now your easiest way to get rid of them is to start giving them warnings based on the animal's behavior. 

My initial thoughts are if you see them and then deny them a discriminatory issue may arise so you better have another reason. 

I denied the applicant in question, and I would deny your application as well.

It's perfectly legal to say your criteria says that people who are swearing at the kids on the voicemail get denied.