Do you ever accept a tenant with a prior eviction?

[Anna Watkins]

I have just told a prospective applicant that a prior eviction is "probably a deal breaker."  She politely said thank you and hung up, but I'm feeling very waffly on this rule.  I know it's standard screening to protect myself, but I also know a lot of good people have had hard times and are trying to come back from them.

I had to evict a tenant about 10 years ago and it was a huge hassle.  I had screened her as best I could, but found out later (from docs left in the filing cabinet left in the house) that she had an eviction history that she hid (it wasn't on her credit report).  On the other side, the most recent tenants in the same house were upfront about a student-loan default, but I accepted them anyway and they were awesome for 3.5 years.

Have you ever had a prospect be upfront with an eviction history, accepted an application anyway and if everything else checked out clean, offer that person a lease?  Is honesty on the applicant's part worth considering as a plus?