This paper investigates test sets with high fault cover-age for multiple stuck-at faults of large combinational cir-cuits and fully scanned sequential circuits. We show an ability of multiple fault detection of test sets generated for single stuck-at faults, then give a procedure for generating a compact test set with high multiple fault coverage. Re-sults show that our method can generate a test set with complete fault coverage for many circuits, and the size of the test set is smaller than previously reported ones.