The most important thing a prospective landlord wants to know and be sure of is, if you move in the space, will you pay each month? Are you used to paying Rent from month to month, without drama, resistance and problems that have to be dealt with? If you are honest with them, you may be able to work out something where they won't run the credit check in lieu of some other proof of a payment history, like your current or past landlord as a reference. The pattern of payment is as important as your income. Good luck.