If interpreted in a strict legal sense, beneficial ownership rules in tax treaties would have no effect on conduit companies because companies at law own their property and income beneficially. Conversely, a company can never own anything in a substantive sense because economically a company is no more than a congeries of arrangements that represents the people behind it. Faced with these contradictory considerations, people have adopted surrogate tests that they attempt to employ in place of the treaty test of beneficial ownership. An example is that treaty benefits should be limited to companies that are both resident in the states that are parties to the treaty and that carry on substantive business activity. The test is inherently illogical. The origins of the substantive business activity test appear to lie in analogies drawn with straw company and base company cases. Because there is no necessary relationship between ownership and activity, the test of substantive business activity can never provide a coherent surrogate for the test of beneficial ownership. The article finishes with a Coda that summarises suggestions for reform to be made in work that is to follow. (authors' abstract) / Series: WU International Taxation Research Paper Series