Fast forward 12 years plus down the road. Your question seems to preclude using a broker. I suspect you don't want to pay a commission. I wonder what your current liabilities are. No doubt landlords will consider every aspect of the prospective renter. That means work history/consistency, income, assets, references and of course credit history. BTW, an owner willing to pay the broker should not be a red flag. Some do it because they want to rent as fast as possible full stop. Good luck.
Landlords bottom line is exactly that, the bottom line. They want to know how will you pay your rent, that is income and how stable you are in your present employment.
It is mostly management companies that will give you a hard time on your credit.
If you have bad credit, can show you are trying to improve it and can explain the negatives, that is in your favor. Honesty, is always the best policy in that situation. As a broker, I appreciate it and so will a potential landlord.
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My suggestion would be to be as honest as possible when applying. Write a short letter to accompany the application, detailing your situation and the circumstances that are "driving" your less than perfect credit score.
As a rental property owner myself, I understand that it's unrealistic to expect everyone to have an 800 credit score. If someone applied who had an unpaid medical bill 5 years ago on their credit report, I'm going to obviously weigh that differently than someone who has recently racked up 5 credit cards and is running from creditors.
Everyone makes mistakes. My credit report was haunted for years by a check I bounced in college from a pizza I ordered at 2AM. Explain your situation - and highlight the fact that you have sufficient income and stellar references from previous landlords. That would, in my opinion, carry much more weight than a mistake you made 6 years ago. The landlord really just wants to know that at the end of the day that currently, you will be able, and willing, to pay your rent when due every month.
Hope that helps!