When landlords run your credit they look at a number of things. For one they look at how much debt you are carrying to see if you can even afford the rent. They also look to see if you have a bunch of things in collections (especially recently) to see if you are the type of person that skips out on their creditors. They also look for judgments against you which is where past broken leases would show up. Each landlord /management company has their own equation of who qualifies and who does not. From what you have described I doubt you will have the slightest problem just as long as you aren’t a sex offender.