Least worst of the crowd?

[Jimmy NA]

As a landlord, I have been thrown a few curve balls and learned as time passed. I operate in a new area and have been shocked by the type of potential tenants I have been encountering to fill my units. I knew it was a low income area I would be in but....darn these people have every social ill imaginable: drugs, alcohol problems, no jobs, single parents with 3-4 kids, etc. Some potential tenants have a combo of these issues. I guess I am asking what should I focus on? Credit? Passsed references? Should I take the least worst of the lot and just accept that this is the clientele I will be dealing with? Thanks to MikeOH and others on this site, I bought right. I can leave a unit vacant for awhile and not be hurt financially very much.
Should I just stay focused and wait till I find someone that meets my standards or re-evalute my standards?