The Hicksian definition of complementarity and substitutability may not apply in contexts in which agents are not utility maximisers or where price or income vari- ations, whether implicit or explicit, are not available. We look for tools to identify complementarity and substitutability satisfying the following criteria: they are be- havioural (based only on observable choice data); model-free (valid whether the agent is rational or not); and they do not rely on price or income variation. We uncover a conflict between properties that it is arguably reasonable for a complementarity notion to possess. We discuss three different possible resolutions of the conflict.