The so-called Internally Headed Relative Clause (IHRC) construction found in the head-final languages Korean and Japanese has received little attention from computational perspectives even though it is frequently found in both text and speech. This is partly because there have been no grammars precise enough to allow deep processing of the construction's syntactic and semantic properties. This paper shows that the typed feature structure grammar HPSG (together with the semantic representations of Minimal Recursion Semantics) offers a computationally feasible and useful way of deep-parsing the construction in question.