Choosing between qualified applicants?

[Christopher Lightner]

Hey everyone, I've got a question about my situation. I have an applicant that I have screened and accepted to rent my property who is on Section 8. However we haven't signed a lease, and the PHA doesn't seem to be in a rush to get the inspection process rolling so it is looking like she won't be able to move in until after the end of the month. I am still showing the property and accepting applications in case she decides to pick another house, so my question is this.

What do I do if another, better qualified applicant comes along who has the funds to pay the deposit and rent on hand and sign a lease in the next few days?

There isn't a signed lease in play, but there is a lot of verbal goodwill between myself and the applicant.