A popular view presents explanations in the cognitive sciences as causal or mechanistic and argues that an important feature of such explanations is that they allow us to manipulate and control the explanandum phenomena. Nonetheless, whether there can be explanations in the cognitive sciences that are neither causal nor mechanistic is still under debate. Another prominent view suggests that both causal and non-causal relations of counterfactual dependence can be explanatory, but this view is open to the criticism that it is not clear how to distinguish explanatory from non-explanatory relations. In this paper, I draw from both views and suggest that, in the cognitive sciences, relations of counterfactual dependence that allow manipulation and control can be explanatory even when they are neither causal nor mechanistic. Furthermore, the ability to allow manipulation can determine whether non-causal counterfactual dependence relations are explanatory. I present a preliminary framework for manipulation relations that includes some non-causal relations and use two examples from the cognitive sciences to show how this framework distinguishes between explanatory and non-explanatory, non-causal relations. The proposed framework suggests that, in the cognitive sciences, causal and non-causal relations have the same criterion for explanatory value, namely, whether or not they allow manipulation and control.