By selecting the most qualified candidate applicant, based on your screening qualifications, and by doing so eliminate a applicant with any type of handicap animal you are not discriminating.If, based on the flexibility of the guidelines for screening, a landlord can not find a way to exclude any and all applicants they wish, without openly discriminating, they have not thoroughly screened.If you do your job correctly you should have no fear of having broken any rules. 

Are your qualifications for tenants too difficult to meet?

That goes to the point, which I find mildly interesting, that being a QI isn't like being a CPA where you have to have some qualification to do the act, but rather anyone excepted a certain class of people can be a QI. 

The problem is dealing with buyers directly is hard enough as they can be flaky even if they have money and are qualifed to do something.

Let your first applicant be a protected class and apply when you jack the income requirement up to 4X and see what happens, it's sure going to look like you jacked the qualification up beyond reasonable and customary to deny them!!!

Tenants still have to meet other qualifications, but in many cities and some entire states, you cannot discriminate based on sources of income, so to deny a tenant only because they will be paying with a voucher is illegal.

Now with our strict rules and qualifications we have a less then 2% eviction rate on over 400 homes.

It covers the minimum qualifications necessary to rent. 

So, if someone otherwise meets rental qualifications here they can't be turned down simply on the basis of the fact they're Section 8 recipients because it's legally obtained income.You may want to have a conversation with a Real Estate lawyer in your home state prior to declining a tenant on the basis that they're a Section 8 recipient. 

Biggest thing I would say is that you should write down your tenant qualifications and your policies for late rent and other things.