This paper pursues two inter-related goals. One goal is to compare the (de)merits of two approaches to the syntax-semantics of Japanese internally-headed relative clauses (IHRCs), one developed by Alexander Grosu, Koji Hoshi, and Fred Landman in a number of earlier studies, and one proposed by Kitagawa ( 2019), with respect to the following issues: [i] the status of the relative clause (non-restrictive or predicate-denoting?); [ii] the status of island-constraints (absolute or subject to cross-idiolectal variation?); and [iii] the infelicitous status of IHRCs with referential IHs (absolute or subject to cross-idiolectal variation?). The paper argues: [a] that the relative clause of an IHRC is predicate-denoting, and [b] that the cross-linguistic variation observed in relation to island-constraints and the (in)felicity of IHRCs with referential IHs is due to the existence of an alternative parse for prima facie IHRCs with referential IHs, in particular, as a special variety of doubly-headed relative constructions (DHRCs). The second goal, which grows out of the need to construct the supporting argumentation for [b], is to establish which properties of DHRCs are shared by IHRCs and which are not, and to construct an explicit compositional analysis of DHRCs that captures this state of affairs. To the best of our knowledge, a compositional analysis of Japanese DHRCs has never been attempted in the earlier literature.