Semi-compositional verb–noun constructions have been investigated under various labels in the different linguistic traditions. In this article we start from the quite well defined notion of support verb construction to present a battery of linguistic tests to distinguish truly semi-compositional constructions from semantically compositional verb–noun combinations on the one hand and from idiomatic constructions on the other. The tests are not genuinely designed by the author but collected from various linguistic investigations on such constructions. As the concept of support verb construction spans across a wide variety of languages, most tests can be applied to several languages. In the article, examples are given for French, English and German. It will be shown that most of the tests that cover the grammaticality of syntactic or semantic transformations of verb–noun constructions only present an approximation of underlying semantic properties and that to almost each alleged property exceptions can be found. However, taken as a whole, the test battery seems to be suitable to delineate support verb constructions from superficially similar linguistic expressions.