Across languages, modal constructions are often ambiguous. It has been observed by Ha (2007) that a modal expression swu ‘way/possibility’ + iss ‘exist’ (‘CAN’) in Korean can be ambiguous between Root Modality and Epistemic Modality. In this paper, I argue that the distinction between Root Modality and Epistemic Modality lies in an adnominal T that bound noun swu takes and theta-role assigning capability of small n with the bound noun: specifically, in the case of Root Modality, the adnominal T takes VP (but not vP) without an external argument, and a bound noun assigns a theta-role to the external argument. On the other hand, in the case of Epistemic Modality, the adnominal T takes vP with an external argument, and a bound noun does not assign a theta-role.