The interaction of a modal auxiliary with tense or aspect components often gives rise to some unexpected inferences. In Korean, when a necessity priority modal –eya ha– ‘should’ is combined with past tense morphology, the sentence yields the ‘non-actualization’ inference. Condoravdi (2002) examines that the similar phenomenon in English. Focusing on the epistemic modal-perfect combination, she proposes a scope-based analysis, and argues that counterfactuality arises as a conversational implicature. I show that, even though Condoravdi’s scope-reversal analysis well explains the counterfactual reading from might have sentences, this account cannot be extended to the Korean data. In my analysis, the non-actualization inference found in priority modal sentences in Korean is a not-at-issue assertion, and this inference arises from the temporal relations between SIT-T, MOD-T and UT-T.