We study properties of a subset of single stuck-at faults defined based on dominance relations and referred to as maximally dominating faults. These faults were shown to be effective in n -detection test generation and in diagnosis. The properties described here can be useful in additional applications. We suggest two such applications. The first is weighted random pattern generation using three weights, 0, 0.5 and 1. The second application is static test compaction that drops unnecessary tests from a given test set in order to reduce its size.