One challenge to lexical (or, more specifically, morphological) integrity – and more generally to compositionality of meaning – is bracketing paradox. Sized inalienable possession (SIP) in Japanese (e.g. ko-kubi ‘small-neck’ in [VP [NPko-kubi-o] kasigeru] ‘small-neck-acc tilt’) is an instance of bracketing paradox where morphological bracketing (such as above) and semantic bracketing (below) conflict with each other. Specifically, a prefix like ko- above acts as an adverbial modifier for a VP, not as a nominal modifier (i.e. [VP slightly (ko) [VP neck tilt]] ‘tilt one's neck slightly’). It is proposed that: (a) syntactically, an SIP expression and its ‘host’ verb are collocationally dependent, and (b) Semantically, either argument or adjunct SIP expressions are Montagovian functors. They take (or act upon) a predicate meaning as an argument to give rise to an appropriate interpretation. This has the effect of confining the unusual adverbial modification within SIP expressions. Without additional stipulations, the current proposal solves hitherto unnoticed empirical problems faced by previous syntactic accounts. In doing so, it avoids employing mechanisms contradicting morphological integrity, namely LF movement of a bound morpheme or co-indexing a word-internal element. Thus, at least in the domain of SIP, the current approach enables us to remain faithful to morphological integrity. A broader issue touched upon here is how compositional semantics is accomplished when it is superficially violated as above. This paper shows that strict adherence to iconicity between syntax and semantics is by no means a necessity for compositional semantics.