The interventionist account of causation offers a criterion to distinguish causes from non-causes. It also aims at defining various desirable properties of causal relationships, such as specificity, proportionality and stability. Here we apply an information-theoretic approach to these properties. We show that the interventionist criterion of causation is formally equivalent to non-zero specificity, and that there are natural, information-theoretic ways to explicate the distinction between potential and actual causal influence. We explicate the idea that the description of causes should be proportional to that of their effects. Then we draw a distinction between two ideas in the existing literature, the range of invariance of a causal relationship and its stability. The range of invariance is related to specificity and range of causal values. Stability concerns the effect of additional variables on the relationship between some focal pair of cause and effect variables. We show how to distinguish and measure the direct influence of background variables on the effect variable, and their influence on the relationship between the focal cause and the effect variable. Finally, we discuss the limitations of the information-theoretic approach, and offer prospects for complementary approaches.