The following banks and credit unions offer excellent features and benefits. While we recommend them, they are not our top picks for the simple reason that they are not guaranteed banks. They have however helped a lot of people, and may be able to help you too.
They do not use ChexSystems or TeleCheck. Most people are still being approved.
California Community Credit Union
They don't run the ChexSystems just a formal credit report.
Safe 1 Credit Union
They use Deluxe Detect and do not do credit reports unless you apply for a loan.
Federal Employees West Federal Credit Union
We currently use TeleCheck when opening accounts.