Lease companies are typically given direction from the home owner. Home owners generally want a tenant with a good credit history because it means that the renter has a track record of making their payments on time. With that being said many home owners recognize that many renters have blemished credit and that is the primary reason they are renting and not buying a home. You can always negotiate a higher deposit or provide more information about your credit history to help alleviate their concerns.
No Bankruptcies, No Evictions, No Utility Company issues, etc.
First we were told that they didn't want to see any bankruptcies or evictions, but they ran our credit and we had a past utility bill that was not taken care of and we had to put down a larger deposit. It all depends on the real estate agent.