Interaction testing is widely used in screening for faults. In software testing, it provides a natural mechanism for testing systems to be deployed on a variety of hardware and software configurations. Several algorithms published in the literature are used as tools to automatically generate these test suites; AETG is a well known example of a family of greedy algorithms that generate one test at a time. In many applications where interaction testing is needed, the entire test suite is not run as a result of time or cost constraints. In these situations, it is essential to prioritize the tests. Here we adapt a "one-test-at-a-time" greedy method to take importance of pairs into account. The method can be used to generate a set of tests in order, so that when run to completion all pairwise interactions are tested, but when terminated after any intermediate number of tests, those deemed most important are tested. Computational results on the method are reported.