The need for testing-for-diagnosis strategies has been identified for a long time, but the explicit link from testing to diagnosis is rare. Here, we start with the study of an algorithm for fault localization that consists of cross-checking information collected from test cases execution traces. Analyzing the type of information needed for an efficient localization, we identify the attribute (called Dynamic Basic Block) that restricts the accuracy of a diagnosis algorithm. Based on this attribute, a test criterion is proposed and validated through rigorous case studies: it shows that test cases can be completed to reach a high level of diagnosis accuracy. So, the dilemma between a reduced testing effort (with as few test cases as possible) and the diagnosis accuracy (that needs as much test cases as possible to get more information) is partly solved by selecting only test cases relevant for diagnosis.