Have you already selected a builder? 

Getting less every month is still generally more cost effective than dealing with a tenant that stops paying or causes damages to the property.However, if you do decide to change your selection criteria and you are worried about fair housing, the main thing is documentation.

It's all the agents that leave your lights and heat/a.c. on and doors wide open.  

Before I could move the door swung wide open and then slammed shut.

You can’t selectively apply the loss.

It may limit your property manager's ability to select the best tenant.

Take advantage of this, explore widely, and look for the right property at the right price.

You want to grow your portfolio wide, before you grow it deep.

At REI Capital Fund LLC, we’ve worked with a wide range of investors, from those flipping their first property to those building large rental portfolios.

When you select the next tenant I would certainly ensure that you have your eyes on the applications that are coming in, and ask that you are involved in the decision making process. 3x income, clean credit and background checks should be a minimum for approval, even if it takes a month or so to find someone.