Grosu & Hoshi (2019:20), in their rejoinder to Kitagawa (2019), propose that apparent violations of island constraints in the so-called internally-headed relative clauses are accounted for by considering them as reduced doubly-headed relative clauses. This paper shows that this claim by Grosu and Hoshi is not empirically sustainable, and further that it misses the discourse function of doubly-headed relative clauses. A discussion of gapless light-headed externally-headed relative clauses is also presented so as to identify how this construction type interrelates with internally-headed relative clauses and doubly-headed relative clauses.