Shawn its a very hard call to make , if you can go back two or three LLs and ask questions you might be able to learn more, there is the rare instance where someone has had medical bills that has caused them alot of money problems . I would only tell you that beside the credit history if criminal background checks come back okay and former LLs and mean going back to the one they rented from BEFORE they were at last residence. Also too its not unheard of to collect first and last months rent and deposit , and keep it month to month, You really can safely ask a former LL and I mean 2nd or 3rd back ,`I have a rental application from a Jane and John doe who rented from you from august 2006 to july 31 2007 ? is this true ?? if they came to you and asked to rent from you again would you re rent to them again? your not asking if they damaged the unit , your not asking if they were late. Just like with any other tenant who is new if you let anything like a late payment slide by then your setting your self up to be taken advantage of. On the other end of things you could have a applicant with a great credit score who turns into the draculawolfstein every full moon becoming such a major headache that you want to pull hair out!