I use TenantBackgroundSearch.com and the site emails the tenant for authorization to run the credit/criminal search.  

Never the one they give you.I would also include no criminal history.  

Note that the mafia doesn't bother trying to extort other criminals, they focus on offering "protection" to the law-abiding small business owner.

They do criminal and credit checks.

If you plan on being in business long term cash for keys is not a appropriate business approach to dealing with criminal tenants.

I see it as another government power grab over landlords and instead of making it easier for us and protect the owner of the property, the criminals win more power over us who are trying to make a living with the rental business.

I focus on describing the actual property itself.However there are some numbers in the ad that will screen out some applicants, such as "One year lease only, first, last, and security deposit due upon lease signing" and "application includes criminal/credit/eviction history screening and employment/income verification". 

Establish your screening criteria; income, criminal history, credit, etc. and stick to that.

I will rent to poor people who can handle the rent, don't have criminal baggage, and no eviction history.

And can't you find tenants who don't know criminals the cops are looking for?