Best practice is to be completely HONEST on your application for rental. Certain considerations are made for certain actions. Unexpected medical issues, low overall scores, even bankruptcy usually can be covered by extra deposit or increased deposits. Every agent and/or agency must provide you with their credit criteria if you ask for it. Most companies post theirs online so you have easy, readily available access to it prior to making an offer. If you have had an eviction, make a payment plan with the owner, landlord or representative of the unit to satisfy your debt. Do it in writing and have it signed by the representative and then make small payments or whatever you can timely and regularly so that when the eviction shows up you have proof that you are meeting your obligations. Some if not all companies see this as positive action to a bad situation and will consider you for tenancy based on the payments being made.
If there are minor issues - such as an unexpected medical bill, or something that can be explained, you might be able to rent with a "slighty" bigger deposit.
If you have been evicted from multiple properties for non-payment of rent, or recently charged a bunch of credit cards up to the moon and are running from creditors........well, that's a different story.
The bottom line is it all depends on how risk-averse the landlord is, and the specifics of your credit history. Every property and situation is different.
Hope that helps!
Long answer = every property is different, but properties that are marketed by owners themselves will have some flexibility in the kind of checks that are done on potential tenants. Properties managed by a professional property management company will almost always run credit and background checks.
Don Moriarty, Broker Classic Texas Properties 512-413-5599