Dispositional actualism (DA) has the theoretical advantage over many other theories in the metaphysics of modality that it successfully grounds the modalities on some thisworldly empirically accessible entities, the dispositions or potentials of things and persons. But previous accounts also suffer from serious problems. We argue for a new account of dispositional actualism that avoids these problems; we call it Cognitive Capacities DA account (CDA); it centres upon a disjunctive analysis of modality that includes cognitive powers in addition to physical powers. This account is recommended not only because of its high intuitive plausibility, demonstrated by the close connection between modality and cognition that has been accepted by many philosophers over the centuries. First and foremost, as we claim, it guarantees for maximal material adequacy of the analysis of modality. Our theses are as follows: (I) Cognitive capacities in which some modalities are grounded are cognitive powers or bundles of interacting cognitive powers which together manifest themselves in a cognitive output. (II) Both metaphysical and logical modalities can be analysed in terms of these cognitive capacities. Finally, (III) an analysis of modalities should be framed in terms of both physical powers and cognitive capacities to have maximal material adequacy.