This paper analyzes a competitive credit market where banks use imperfect and independent tests to assess the ability of a potential creditor to repay credit. The banks compete by announcing interest rates at which they will provide credit to those applicants who pass the banks' tests. The proportion of applicants who pass the test of at least one bank increases with the number of banks providing credit, so the average credit-worthiness decreases. It is then shown that in a situation where all banks charge the same interest rate, a bank always has the incentive to undercut in order to improve the average credit-worthiness of its own clientele. This feature represents the major difference from the situations in standard Bertrand and Bertrand-Edgeworth models.