A schedulability test is defined to be sustainable if any task system deemed schedulable by the test remains so if it behaves "better" than mandated by its system specifications. We provide a formal definition of sustainability, and subject the concept to systematic analysis in the context of the uniprocessor scheduling of periodic and sporadic task systems. We argue that it is in general good engineering practice to use sustainable tests if possible, and classify common uniprocessor schedulability tests according to whether they are sustainable or not.