The causal structure underlying an experiment may lead to device-independent constraints on the possible correlations between variables describing the experiment, yielding a separation between classical, quantum, and general-probabilistic correlations. The Bell scenario provides one of the earliest and simplest illustration of this general feature. Many subsequent works have investigated more complicated causal structures than the one assumed in the Bell scenario, providing new examples of how quantum theory deviates from classical physics in a device-independent setting. In this talk, I consider whether there are simpler causal structures than the one assumed in the Bell scenario that nevertheless also lead to a separation between classical and quantum correlations. The results by Henson, Lal, and Pusey imply that the “instrumental scenario” is the only scenario simpler than Bell’s one that can potentially lead to a classical/quantum separation. I will show that the instrumental scenario does indeed lead to such a separation by providing a specific “instrumental inequality” that is satisfied by classical theories but which can be violated by quantum or general-probabilistic theories. Interestingly, this inequality is closely related to the CHSH inequality and provides a new way to test it.