Test coverage criteria define a set of entities of a program flowgraph and require that every entity is covered by some test. We first identify E/sub c/, the set of entities to be covered according to a criterion c, for a family of widely used test coverage criteria. We then present a method to derive a minimum set of entities, called a spanning set, such that a set of test paths covering the entities in this set covers every entity in E/sub c/. We provide a generalised algorithm, which is parametrized by the coverage criterion. We suggest several useful applications of spanning sets of entities to testing. In particular they help to reduce and to estimate the number of tests needed to satisfy test coverage criteria.