Tes t coverage criteria define a set of enti t ies of a program flowgraph and require that every enti ty is covered by some test. In th is paper we first ideniify E,, the set of enti t ies t o be covered according t o a criter ion c , f o r a fami l y of widely used tes t coverage criteria. W e then present a method t o derive a m i n i m u m set of entities, called a spanning set, such that a set of tes t paths covering the enti t ies in this set couers euery en t i ty in E,. W e provide a generalised algorithm, which i s parametrized by the coverage criterion. W e suggest several useful applications of spanning sets of enti t ies t o testing. In particular, they help t o reduce and t o estimate the number of t es t s needed t o satisfy tes t coverage criteria.