In this paper, I argue that counterfactual fairness does not constitute a necessary condition for an algorithm to be fair, and subsequently suggest how the constraint can be modified in order to remedy this shortcoming. To this end, I discuss a hypothetical scenario in which counterfactual fairness and an intuitive judgment of fairness come apart. Then, I turn to the question how the concept of discrimination can be explicated in order to examine the shortcomings of counterfactual fairness as a necessary condition of algorithmic fairness in more detail. I then incorporate the insights of this analysis into a novel fairness constraint, causal relevance fairness, which is a modification of the counterfactual fairness constraint that seems to circumvent its shortcomings.