I hold my skills and abilities regarding ferreting out undesirable applicants as high or higher than you hold your own. 

In my experience, this helps weed out some of the most undesireables right off the bat.Best of Luck!

Month-to-Month agreements do have their advantages as they allow landlords to more easily address non-performance and quickly end tenancies that are undesirable.

You bought a very cheap(undesirable) property in a cheap(undesirable) neighborhood.

I recently wrote to someone in another thread that concern over how to afford it can be taken as a gauge of a person's readiness or suitability to take on an entrepreneurial endeavor.Y'know, I have peripheral neuropathy, and it's REALLY hard to type some of those long words without messing 'em up!

Undesirable properties, and those with other tax lien certs, may go unsold.

In most cases the reason they were not bid on, is they are undesirable and unsalable.

That will limit the amount of responses you get, thus filtering out some of the undesirable tenant situations, and garner you more rent. 

In this case you are not rejecting due to family status, which is protected, you are rejection due to a undesirable fit.

Not all tenants are clearly desirable or undesirable, so if a tenant is just so-so, or is a pain to deal with, and if he's been in place for a while and the property is in need of some cleaning and refurbishment anyway, the landlord might decide to end the lease and start fresh with a tenant paying higher rent.