This paper starts by discussing research into the effect of background knowledge on English for Academic Purposes (EAP) tests and discusses EAP tests in which the content of at least some of the test components is related to students’ fields of academic study. This section shows how research has demonstrated that students do not necessarily do better if they are given tests in their own academic subject areas and how, because of the difficulties inherent in test-equating, such tests may not be testing the students fairly. The paper suggests, therefore, that for international EAP tests, English for Specific Academic Purposes testing be abandoned. In its second part, the paper discusses what EAP tests might consist of in the future. Instead of EAP proficiency tests, the paper suggests that there should be aptitude tests to find out whether L1 and L2 students would be capable of rapidly acquiring the requisite academic discourse practices once they had embarked on their academic courses. Such tests for L2 students should include a test of specific grammatical skills, so that receiving institutions can be sure that students have the requisite linguistic infrastructure needed to carry out academic work in English.