You won't qualify for the "lowest," but you will come very close. Other issues in qualifying are property type, savings, stability, and ratios (both income as well as LTV -- loan to value). Assuming that all of these are ideal, then you'll be within .125% of the best available rates. Lenders now-a-days offer incentives to borrowers by discounting rates/costs for those with credit risk scores over 750. This translates to .5% reduction in closing costs (e.g. on a $100,000 loan amount this is $500).
No matter what, however, you'll find someone who will approve you. Try IndyMac Bank; they have the best available rates and costs.